From ef0b4664272bef276e447f3627e9fe556305e80b Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Wed, 8 Aug 2018 20:55:43 +0800
Subject: [PATCH 01/12] Add customized edge weight support for graphs.

---
 DataStructures/Graphs/CliqueGraph.cs          | 10 ++--
 DataStructures/Graphs/DirectedDenseGraph.cs   |  6 +-
 DataStructures/Graphs/DirectedSparseGraph.cs  |  6 +-
 .../Graphs/DirectedWeightedDenseGraph.cs      | 42 ++++++-------
 .../Graphs/DirectedWeightedSparseGraph.cs     | 52 ++++++++--------
 DataStructures/Graphs/IEdge.cs                |  6 +-
 DataStructures/Graphs/IGraph.cs               | 13 ++--
 DataStructures/Graphs/IWeightedGraph.cs       | 12 ++--
 DataStructures/Graphs/UndirectedDenseGraph.cs |  6 +-
 .../Graphs/UndirectedSparseGraph.cs           |  6 +-
 .../Graphs/UndirectedWeightedDenseGraph.cs    | 48 +++++++--------
 .../Graphs/UndirectedWeightedSparseGraph.cs   | 60 +++++++++----------
 DataStructures/Graphs/UnweightedEdge.cs       |  2 +-
 DataStructures/Graphs/WeightedEdge.cs         | 10 ++--
 14 files changed, 142 insertions(+), 137 deletions(-)

diff --git a/DataStructures/Graphs/CliqueGraph.cs b/DataStructures/Graphs/CliqueGraph.cs
index 2d075564..6f7f3db3 100644
--- a/DataStructures/Graphs/CliqueGraph.cs
+++ b/DataStructures/Graphs/CliqueGraph.cs
@@ -255,7 +255,7 @@ ISet<UnordererPair<T>> getPairs(ICollection<T> vertices)
         /// <summary>
         /// An enumerable collection of all graph edges.
         /// </summary>
-        public IEnumerable<IEdge<T>> Edges
+        public IEnumerable<IEdge<T, Int64>> Edges
         {
             get
             {
@@ -273,7 +273,7 @@ public IEnumerable<IEdge<T>> Edges
         /// <summary>
         /// Get all incoming edges to vertex.
         /// </summary>
-        public IEnumerable<IEdge<T>> IncomingEdges(T vertex)
+        public IEnumerable<IEdge<T, Int64>> IncomingEdges(T vertex)
         {
             List<UnweightedEdge<T>> incomingEdges = new List<UnweightedEdge<T>>();
 
@@ -296,7 +296,7 @@ public IEnumerable<IEdge<T>> IncomingEdges(T vertex)
         /// <summary>
         /// Get all outgoing edges from a vertex.
         /// </summary>
-        public IEnumerable<IEdge<T>> OutgoingEdges(T vertex)
+        public IEnumerable<IEdge<T, Int64>> OutgoingEdges(T vertex)
         {
             List<UnweightedEdge<T>> outgoingEdges = new List<UnweightedEdge<T>>();
 
@@ -394,7 +394,7 @@ public void AddVertices(IEnumerable<T> collection)
         /// Adds a list of vertices to the graph.
         /// </summary>
         /// <param name="collection">Collection.</param>
-        void IGraph<T>.AddVertices(IList<T> collection)
+        void IGraph<T, Int64>.AddVertices(IList<T> collection)
         {
             AddVertices(collection);
         }
@@ -598,7 +598,7 @@ ICollection<UnordererPair<T>> getEdges()
         /// Returns the list of Vertices.
         /// </summary>
         /// <value>The vertices.</value>
-        IEnumerable<T> IGraph<T>.Vertices
+        IEnumerable<T> IGraph<T, Int64>.Vertices
         {
             get
             {
diff --git a/DataStructures/Graphs/DirectedDenseGraph.cs b/DataStructures/Graphs/DirectedDenseGraph.cs
index 264dff1c..caea4be0 100644
--- a/DataStructures/Graphs/DirectedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedDenseGraph.cs
@@ -102,17 +102,17 @@ public virtual IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
diff --git a/DataStructures/Graphs/DirectedSparseGraph.cs b/DataStructures/Graphs/DirectedSparseGraph.cs
index e8ce7df9..a55c6e88 100644
--- a/DataStructures/Graphs/DirectedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedSparseGraph.cs
@@ -92,17 +92,17 @@ public virtual IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
diff --git a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
index 68ea3c5e..521991e8 100644
--- a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
@@ -23,18 +23,18 @@ namespace DataStructures.Graphs
     /// <summary>
     /// This class represents the graph as an adjacency-matrix (two dimensional integer array).
     /// </summary>
-    public class DirectedWeightedDenseGraph<T> : DirectedDenseGraph<T>, IWeightedGraph<T> where T : IComparable<T>
+    public class DirectedWeightedDenseGraph<T, W> : DirectedDenseGraph<T>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// INSTANCE VARIABLES
         /// </summary>
-        private const long EMPTY_EDGE_SLOT = 0;
+        private static readonly W EMPTY_EDGE_SLOT = default(W);
         private const object EMPTY_VERTEX_SLOT = (object)null;
 
         // Store edges and their weights as integers.
         // Any edge with a value of zero means it doesn't exist. Otherwise, it exist with a specific weight value.
         // Default value for positive edges is 1.
-        protected new long[,] _adjacencyMatrix { get; set; }
+        protected new W[,] _adjacencyMatrix { get; set; }
 
 
         /// <summary>
@@ -47,7 +47,7 @@ public DirectedWeightedDenseGraph(uint capacity = 10)
             _verticesCapacity = (int)capacity;
 
             _vertices = new ArrayList<object>(_verticesCapacity);
-            _adjacencyMatrix = new long[_verticesCapacity, _verticesCapacity];
+            _adjacencyMatrix = new W[_verticesCapacity, _verticesCapacity];
             _adjacencyMatrix.Populate(rows: _verticesCapacity, columns: _verticesCapacity, defaultValue: EMPTY_EDGE_SLOT);
         }
 
@@ -57,13 +57,13 @@ public DirectedWeightedDenseGraph(uint capacity = 10)
         /// </summary>
         protected override bool _doesEdgeExist(int source, int destination)
         {
-            return (_adjacencyMatrix[source, destination] != EMPTY_EDGE_SLOT);
+            return (EMPTY_EDGE_SLOT.Equals(_adjacencyMatrix[source, destination]));
         }
 
         /// <summary>
         /// Helper function. Gets the weight of a directed edge.
         /// </summary>
-        private long _getEdgeWeight(int source, int destination)
+        private W _getEdgeWeight(int source, int destination)
         {
             return _adjacencyMatrix[source, destination];
         }
@@ -80,7 +80,7 @@ public override bool IsWeighted
         /// <summary>
         /// An enumerable collection of all weighted directed edges in graph.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> Edges
+        public new virtual IEnumerable<WeightedEdge<T, W>> Edges
         {
             get
             {
@@ -93,7 +93,7 @@ public virtual IEnumerable<WeightedEdge<T>> Edges
         /// <summary>
         /// Get all incoming unweighted edges to a vertex.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
+        public new virtual IEnumerable<WeightedEdge<T, W>> IncomingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
@@ -104,7 +104,7 @@ public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
             {
                 if (_vertices[adjacent] != null && _doesEdgeExist(adjacent, source))
                 {
-                    yield return (new WeightedEdge<T>(
+                    yield return (new WeightedEdge<T, W>(
                         (T)_vertices[adjacent],             // from
                         vertex,                             // to
                         _getEdgeWeight(source, adjacent)    // weight
@@ -116,7 +116,7 @@ public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
         /// <summary>
         /// Get all outgoing unweighted edges from a vertex.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
+        public new virtual IEnumerable<WeightedEdge<T, W>> OutgoingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
@@ -127,7 +127,7 @@ public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
             {
                 if (_vertices[adjacent] != null && _doesEdgeExist(source, adjacent))
                 {
-                    yield return (new WeightedEdge<T>(
+                    yield return (new WeightedEdge<T, W>(
                         vertex,                             // from
                         (T)_vertices[adjacent],             // to
                         _getEdgeWeight(source, adjacent)    // weight
@@ -149,10 +149,10 @@ public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
         /// <summary>
         /// Connects two vertices together with a weight, in the direction: first->second.
         /// </summary>
-        public virtual bool AddEdge(T source, T destination, long weight)
+        public virtual bool AddEdge(T source, T destination, W weight)
         {
             // Return if the weight is equals to the empty edge value
-            if (weight == EMPTY_EDGE_SLOT)
+            if (EMPTY_EDGE_SLOT.Equals(weight))
                 return false;
 
             // Get indices of vertices
@@ -199,10 +199,10 @@ public override bool RemoveEdge(T source, T destination)
         /// <summary>
         /// Updates the edge weight from source to destination.
         /// </summary>
-        public virtual bool UpdateEdgeWeight(T source, T destination, long weight)
+        public virtual bool UpdateEdgeWeight(T source, T destination, W weight)
         {
             // Return if the weight is equals to the empty edge value
-            if (weight == EMPTY_EDGE_SLOT)
+            if (EMPTY_EDGE_SLOT.Equals(weight))
                 return false;
 
             // Get indices of vertices
@@ -271,7 +271,7 @@ public override bool RemoveVertex(T vertex)
         /// <summary>
         /// Get edge object from source to destination.
         /// </summary>
-        public virtual WeightedEdge<T> GetEdge(T source, T destination)
+        public virtual WeightedEdge<T, W> GetEdge(T source, T destination)
         {
             // Get indices of vertices
             int srcIndex = _vertices.IndexOf(source);
@@ -283,13 +283,13 @@ public virtual WeightedEdge<T> GetEdge(T source, T destination)
             if (!_doesEdgeExist(srcIndex, dstIndex))
                 throw new Exception("Edge doesn't exist.");
 
-            return (new WeightedEdge<T>(source, destination, _getEdgeWeight(srcIndex, dstIndex)));
+            return (new WeightedEdge<T, W>(source, destination, _getEdgeWeight(srcIndex, dstIndex)));
         }
 
         /// <summary>
         /// Returns the edge weight from source to destination.
         /// </summary>
-        public virtual long GetEdgeWeight(T source, T destination)
+        public virtual W GetEdgeWeight(T source, T destination)
         {
             return GetEdge(source, destination).Weight;
         }
@@ -297,12 +297,12 @@ public virtual long GetEdgeWeight(T source, T destination)
         /// <summary>
         /// Returns the neighbours of a vertex as a dictionary of nodes-to-weights.
         /// </summary>
-        public virtual Dictionary<T, long> NeighboursMap(T vertex)
+        public virtual Dictionary<T, W> NeighboursMap(T vertex)
         {
             if (!HasVertex(vertex))
                 return null;
 
-            var neighbors = new Dictionary<T, long>();
+            var neighbors = new Dictionary<T, W>();
             int source = _vertices.IndexOf(vertex);
 
             // Check existence of vertex
@@ -351,7 +351,7 @@ public override void Clear()
             _edgesCount = 0;
             _verticesCount = 0;
             _vertices = new ArrayList<object>(_verticesCapacity);
-            _adjacencyMatrix = new long[_verticesCapacity, _verticesCapacity];
+            _adjacencyMatrix = new W[_verticesCapacity, _verticesCapacity];
             _adjacencyMatrix.Populate(rows: _verticesCapacity, columns: _verticesCapacity, defaultValue: EMPTY_EDGE_SLOT);
         }
 
diff --git a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
index 66c0ccfe..5c72cd9d 100644
--- a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
@@ -18,15 +18,15 @@
 
 namespace DataStructures.Graphs
 {
-    public class DirectedWeightedSparseGraph<T> : IGraph<T>, IWeightedGraph<T> where T : IComparable<T>
+    public class DirectedWeightedSparseGraph<T, W> : IGraph<T, W>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// INSTANCE VARIABLES
         /// </summary>
-        private const long EMPTY_EDGE_VALUE = 0;
+        private static readonly W EMPTY_EDGE_VALUE = default(W);
         protected virtual int _edgesCount { get; set; }
         protected virtual T _firstInsertedNode { get; set; }
-        protected virtual Dictionary<T, DLinkedList<WeightedEdge<T>>> _adjacencyList { get; set; }
+        protected virtual Dictionary<T, DLinkedList<WeightedEdge<T, W>>> _adjacencyList { get; set; }
 
 
         /// <summary>
@@ -37,19 +37,19 @@ public DirectedWeightedSparseGraph() : this(10) { }
         public DirectedWeightedSparseGraph(uint initialCapacity)
         {
             _edgesCount = 0;
-            _adjacencyList = new Dictionary<T, DLinkedList<WeightedEdge<T>>>((int)initialCapacity);
+            _adjacencyList = new Dictionary<T, DLinkedList<WeightedEdge<T, W>>>((int)initialCapacity);
         }
 
 
         /// <summary>
         /// Helper function. Returns edge object from source to destination, if exists; otherwise, null.
         /// </summary>
-        protected virtual WeightedEdge<T> _tryGetEdge(T source, T destination)
+        protected virtual WeightedEdge<T, W> _tryGetEdge(T source, T destination)
         {
-            WeightedEdge<T> edge = null;
+            WeightedEdge<T, W> edge = null;
 
             // Predicate
-            var sourceToDestinationPredicate = new Predicate<WeightedEdge<T>>((item) => item.Source.IsEqualTo<T>(source) && item.Destination.IsEqualTo<T>(destination));
+            var sourceToDestinationPredicate = new Predicate<WeightedEdge<T, W>>((item) => item.Source.IsEqualTo<T>(source) && item.Destination.IsEqualTo<T>(destination));
 
             // Try to find a match
             if(_adjacencyList.ContainsKey(source))
@@ -72,7 +72,7 @@ protected virtual bool _doesEdgeExist(T source, T destination)
         /// Helper function. Gets the weight of a directed edge.
         /// Presumes edge does already exist.
         /// </summary>
-        private long _getEdgeWeight(T source, T destination)
+        private W _getEdgeWeight(T source, T destination)
         {
             return _tryGetEdge(source, destination).Weight;
         }
@@ -123,17 +123,17 @@ public IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        IEnumerable<IEdge<T, W>> IGraph<T, W>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T, W>> IGraph<T, W>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T, W>> IGraph<T, W>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
@@ -142,7 +142,7 @@ IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         /// <summary>
         /// An enumerable collection of all directed weighted edges in graph.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> Edges
+        public virtual IEnumerable<WeightedEdge<T, W>> Edges
         {
             get
             {
@@ -155,16 +155,16 @@ public virtual IEnumerable<WeightedEdge<T>> Edges
         /// <summary>
         /// Get all incoming directed weighted edges to a vertex.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
+        public virtual IEnumerable<WeightedEdge<T, W>> IncomingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
 
-            var predicate = new Predicate<WeightedEdge<T>>((edge) => edge.Destination.IsEqualTo(vertex));
+            var predicate = new Predicate<WeightedEdge<T, W>>((edge) => edge.Destination.IsEqualTo(vertex));
 
             foreach(var adjacent in _adjacencyList.Keys)
             {
-                WeightedEdge<T> incomingEdge = null;
+                WeightedEdge<T, W> incomingEdge = null;
 
                 if (_adjacencyList[adjacent].TryFindFirst(predicate, out incomingEdge))
                     yield return incomingEdge;
@@ -174,7 +174,7 @@ public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
         /// <summary>
         /// Get all outgoing directed weighted edges from a vertex.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
+        public virtual IEnumerable<WeightedEdge<T, W>> OutgoingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
@@ -196,10 +196,10 @@ public bool AddEdge(T source, T destination)
         /// <summary>
         /// Connects two vertices together with a weight, in the direction: first->second.
         /// </summary>
-        public bool AddEdge(T source, T destination, long weight)
+        public bool AddEdge(T source, T destination, W weight)
         {
             // Check existence of nodes, the validity of the weight value, and the non-existence of edge
-            if (weight == EMPTY_EDGE_VALUE)
+            if (EMPTY_EDGE_VALUE.Equals(weight))
                 return false;
             if (!HasVertex(source) || !HasVertex(destination))
                 return false;
@@ -207,7 +207,7 @@ public bool AddEdge(T source, T destination, long weight)
                 return false;
 
             // Add edge from source to destination
-            var edge = new WeightedEdge<T>(source, destination, weight);
+            var edge = new WeightedEdge<T, W>(source, destination, weight);
             _adjacencyList[source].Append(edge);
 
             // Increment edges count
@@ -241,10 +241,10 @@ public virtual bool RemoveEdge(T source, T destination)
             return true;
         }
 
-        public bool UpdateEdgeWeight(T source, T destination, long weight)
+        public bool UpdateEdgeWeight(T source, T destination, W weight)
         {
             // Check existence of vertices and validity of the weight value
-            if (weight == EMPTY_EDGE_VALUE)
+            if (EMPTY_EDGE_VALUE.Equals(weight))
                 return false;
             if (!HasVertex(source) || !HasVertex(destination))
                 return false;
@@ -264,7 +264,7 @@ public bool UpdateEdgeWeight(T source, T destination, long weight)
         /// <summary>
         /// Get edge object from source to destination.
         /// </summary>
-        public virtual WeightedEdge<T> GetEdge(T source, T destination)
+        public virtual WeightedEdge<T, W> GetEdge(T source, T destination)
         {
             if (!HasVertex(source) || !HasVertex(destination))
                 throw new KeyNotFoundException("Either one of the vertices or both of them don't exist.");
@@ -282,7 +282,7 @@ public virtual WeightedEdge<T> GetEdge(T source, T destination)
         /// <summary>
         /// Returns the edge weight from source to destination.
         /// </summary>
-        public virtual long GetEdgeWeight(T source, T destination)
+        public virtual W GetEdgeWeight(T source, T destination)
         {
             return GetEdge(source, destination).Weight;
         }
@@ -310,7 +310,7 @@ public virtual bool AddVertex(T vertex)
             if (_adjacencyList.Count == 0)
                 _firstInsertedNode = vertex;
 
-            _adjacencyList.Add(vertex, new DLinkedList<WeightedEdge<T>>());
+            _adjacencyList.Add(vertex, new DLinkedList<WeightedEdge<T, W>>());
 
             return true;
         }
@@ -383,13 +383,13 @@ public virtual DLinkedList<T> Neighbours(T vertex)
         /// <summary>
         /// Returns the neighbours of a vertex as a dictionary of nodes-to-weights.
         /// </summary>
-        public Dictionary<T, long> NeighboursMap(T vertex)
+        public Dictionary<T, W> NeighboursMap(T vertex)
         {
             if (!HasVertex(vertex))
                 return null;
 
             var neighbors = _adjacencyList[vertex];
-            var map = new Dictionary<T, long>(neighbors.Count);
+            var map = new Dictionary<T, W>(neighbors.Count);
 
             foreach (var adjacent in neighbors)
                 map.Add(adjacent.Destination, adjacent.Weight);
diff --git a/DataStructures/Graphs/IEdge.cs b/DataStructures/Graphs/IEdge.cs
index 35371119..ad9bb615 100644
--- a/DataStructures/Graphs/IEdge.cs
+++ b/DataStructures/Graphs/IEdge.cs
@@ -5,7 +5,7 @@ namespace DataStructures.Graphs
     /// <summary>
     /// This interface should be implemented by all edges classes.
     /// </summary>
-    public interface IEdge<TVertex> : IComparable<IEdge<TVertex>> where TVertex : IComparable<TVertex>
+    public interface IEdge<TVertex, TWeight> : IComparable<IEdge<TVertex, TWeight>> where TVertex : IComparable<TVertex>
     {
         /// <summary>
         /// Gets a value indicating whether this edge is weighted.
@@ -30,7 +30,9 @@ public interface IEdge<TVertex> : IComparable<IEdge<TVertex>> where TVertex : IC
         /// Unwighted edges can be thought of as edges of the same weight
         /// </summary>
         /// <value>The weight.</value>
-        Int64 Weight { get; set; }
+        TWeight Weight { get; set; }
     }
+
+    public interface IEdge<TVertex> : IEdge<TVertex, Int64> where TVertex : IComparable<TVertex> { }
 }
 
diff --git a/DataStructures/Graphs/IGraph.cs b/DataStructures/Graphs/IGraph.cs
index 1ae595cc..aba12999 100644
--- a/DataStructures/Graphs/IGraph.cs
+++ b/DataStructures/Graphs/IGraph.cs
@@ -1,11 +1,11 @@
 using System;
 using System.Collections.Generic;
-
 using DataStructures.Lists;
+using System.Linq;
 
 namespace DataStructures.Graphs
 {
-    public interface IGraph<T> where T : IComparable<T>
+    public interface IGraph<T, W> where T : IComparable<T>
     {
         /// <summary>
         /// Returns true, if graph is directed; false otherwise.
@@ -35,17 +35,17 @@ public interface IGraph<T> where T : IComparable<T>
         /// <summary>
         /// An enumerable collection of edges.
         /// </summary>
-        IEnumerable<IEdge<T>> Edges { get; }
+        IEnumerable<IEdge<T, W>> Edges { get; }
 
         /// <summary>
         /// Get all incoming edges from vertex
         /// </summary>
-        IEnumerable<IEdge<T>> IncomingEdges(T vertex);
+        IEnumerable<IEdge<T, W>> IncomingEdges(T vertex);
 
         /// <summary>
         /// Get all outgoing edges from vertex
         /// </summary>
-        IEnumerable<IEdge<T>> OutgoingEdges(T vertex);
+        IEnumerable<IEdge<T, W>> OutgoingEdges(T vertex);
 
         /// <summary>
         /// Connects two vertices together.
@@ -124,5 +124,6 @@ public interface IGraph<T> where T : IComparable<T>
         /// </summary>
         void Clear();
     }
-}
 
+    public interface IGraph<T> : IGraph<T, Int64> where T : IComparable<T> { }
+}
diff --git a/DataStructures/Graphs/IWeightedGraph.cs b/DataStructures/Graphs/IWeightedGraph.cs
index 66f3a857..c994edb4 100644
--- a/DataStructures/Graphs/IWeightedGraph.cs
+++ b/DataStructures/Graphs/IWeightedGraph.cs
@@ -5,32 +5,32 @@ namespace DataStructures.Graphs
     /// <summary>
     /// This interface should be implemented alongside the IGraph interface.
     /// </summary>
-    public interface IWeightedGraph<T> where T : IComparable<T>
+    public interface IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// Connects two vertices together with a weight, in the direction: first->second.
         /// </summary>
-        bool AddEdge(T source, T destination, long weight);
+        bool AddEdge(T source, T destination, W weight);
 
         /// <summary>
         /// Updates the edge weight from source to destination.
         /// </summary>
-        bool UpdateEdgeWeight(T source, T destination, long weight);
+        bool UpdateEdgeWeight(T source, T destination, W weight);
 
         /// <summary>
         /// Get edge object from source to destination.
         /// </summary>
-        WeightedEdge<T> GetEdge(T source, T destination);
+        WeightedEdge<T, W> GetEdge(T source, T destination);
 
         /// <summary>
         /// Returns the edge weight from source to destination.
         /// </summary>
-        long GetEdgeWeight(T source, T destination);
+        W GetEdgeWeight(T source, T destination);
 
         /// <summary>
         /// Returns the neighbours of a vertex as a dictionary of nodes-to-weights.
         /// </summary>
-        System.Collections.Generic.Dictionary<T, long> NeighboursMap(T vertex);
+        System.Collections.Generic.Dictionary<T, W> NeighboursMap(T vertex);
     }
 }
 
diff --git a/DataStructures/Graphs/UndirectedDenseGraph.cs b/DataStructures/Graphs/UndirectedDenseGraph.cs
index f6526541..55f7d212 100644
--- a/DataStructures/Graphs/UndirectedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedDenseGraph.cs
@@ -108,17 +108,17 @@ public virtual IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
diff --git a/DataStructures/Graphs/UndirectedSparseGraph.cs b/DataStructures/Graphs/UndirectedSparseGraph.cs
index 3593c0ec..06a50d9b 100644
--- a/DataStructures/Graphs/UndirectedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedSparseGraph.cs
@@ -93,17 +93,17 @@ public virtual IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
diff --git a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
index c26094ca..d3f6fb16 100644
--- a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
@@ -21,18 +21,18 @@ namespace DataStructures.Graphs
     /// <summary>
     /// This class represents the graph as an adjacency-matrix (two dimensional integer array).
     /// </summary>
-    public class UndirectedWeightedDenseGraph<T> : UndirectedDenseGraph<T>, IWeightedGraph<T> where T : IComparable<T>
+    public class UndirectedWeightedDenseGraph<T, W> : UndirectedDenseGraph<T>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// INSTANCE VARIABLES
         /// </summary>
-        private const long EMPTY_EDGE_SLOT = 0;
+        private static readonly W EMPTY_EDGE_SLOT = default(W);
         private const object EMPTY_VERTEX_SLOT = (object)null;
 
         // Store edges and their weights as integers.
         // Any edge with a value of zero means it doesn't exist. Otherwise, it exist with a specific weight value.
         // Default value for positive edges is 1.
-        protected new long[,] _adjacencyMatrix { get; set; }
+        protected new W[,] _adjacencyMatrix { get; set; }
 
 
         /// <summary>
@@ -45,7 +45,7 @@ public UndirectedWeightedDenseGraph(uint capacity = 10)
             _verticesCapacity = (int)capacity;
 
             _vertices = new ArrayList<object>(_verticesCapacity);
-            _adjacencyMatrix = new long[_verticesCapacity, _verticesCapacity];
+            _adjacencyMatrix = new W[_verticesCapacity, _verticesCapacity];
             _adjacencyMatrix.Populate(rows: _verticesCapacity, columns: _verticesCapacity, defaultValue: EMPTY_EDGE_SLOT);
         }
 
@@ -55,15 +55,15 @@ public UndirectedWeightedDenseGraph(uint capacity = 10)
         /// </summary>
         protected override bool _doesEdgeExist(int source, int destination)
         {
-            return (_adjacencyMatrix[source, destination] != EMPTY_EDGE_SLOT) || (_adjacencyMatrix[destination, source] != EMPTY_EDGE_SLOT);
+            return (!EMPTY_EDGE_SLOT.Equals(_adjacencyMatrix[source, destination])) || (!EMPTY_EDGE_SLOT.Equals(_adjacencyMatrix[destination, source]));
         }
 
         /// <summary>
         /// Helper function. Gets the weight of a undirected edge.
         /// </summary>
-        private long _getEdgeWeight(int source, int destination)
+        private W _getEdgeWeight(int source, int destination)
         {
-            return (_adjacencyMatrix[source, destination] != EMPTY_EDGE_SLOT ? _adjacencyMatrix[source, destination] : _adjacencyMatrix[destination, source]);
+            return (!EMPTY_EDGE_SLOT.Equals(_adjacencyMatrix[source, destination]) ? _adjacencyMatrix[source, destination] : _adjacencyMatrix[destination, source]);
         }
 
 
@@ -78,7 +78,7 @@ public override bool IsWeighted
         /// <summary>
         /// An enumerable collection of edges.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> Edges
+        public new virtual IEnumerable<WeightedEdge<T, W>> Edges
         {
             get
             {
@@ -104,7 +104,7 @@ public virtual IEnumerable<WeightedEdge<T>> Edges
                                 continue;
                             seen.Add(outgoingEdge);
 
-                            yield return (new WeightedEdge<T>(outgoingEdge.Key, outgoingEdge.Value, weight));
+                            yield return (new WeightedEdge<T, W>(outgoingEdge.Key, outgoingEdge.Value, weight));
                         }
                     }
                 }//end-foreach
@@ -114,7 +114,7 @@ public virtual IEnumerable<WeightedEdge<T>> Edges
         /// <summary>
         /// Get all incoming edges to a vertex
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
+        public new virtual IEnumerable<WeightedEdge<T, W>> IncomingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
@@ -125,7 +125,7 @@ public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
             {
                 if (_vertices[adjacent] != null && _doesEdgeExist(source, adjacent))
                 {
-                    yield return (new WeightedEdge<T>(
+                    yield return (new WeightedEdge<T, W>(
                         (T)_vertices[adjacent],             // from
                         vertex,                             // to
                         _getEdgeWeight(source, adjacent)    // weight
@@ -137,7 +137,7 @@ public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
         /// <summary>
         /// Get all outgoing weighted edges from vertex
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
+        public new virtual IEnumerable<WeightedEdge<T, W>> OutgoingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
@@ -148,7 +148,7 @@ public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
             {
                 if (_vertices[adjacent] != null && _doesEdgeExist(source, adjacent))
                 {
-                    yield return (new WeightedEdge<T>(
+                    yield return (new WeightedEdge<T, W>(
                         vertex,                             // from
                         (T)_vertices[adjacent],             // to
                         _getEdgeWeight(source, adjacent)    // weight
@@ -170,10 +170,10 @@ public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
         /// <summary>
         /// Connects two vertices together with a weight, in the direction: first->second.
         /// </summary>
-        public virtual bool AddEdge(T source, T destination, long weight)
+        public virtual bool AddEdge(T source, T destination, W weight)
         {
             // Return if the weight is equals to the empty edge value
-            if (weight == EMPTY_EDGE_SLOT)
+            if (EMPTY_EDGE_SLOT.Equals(weight))
                 return false;
 
             // Get indices of vertices
@@ -223,10 +223,10 @@ public override bool RemoveEdge(T source, T destination)
         /// <summary>
         /// Updates the edge weight from source to destination.
         /// </summary>
-        public virtual bool UpdateEdgeWeight(T source, T destination, long weight)
+        public virtual bool UpdateEdgeWeight(T source, T destination, W weight)
         {
             // Return if the weight is equals to the empty edge value
-            if (weight == EMPTY_EDGE_SLOT)
+            if (EMPTY_EDGE_SLOT.Equals(weight))
                 return false;
 
             // Get indices of vertices
@@ -240,7 +240,7 @@ public virtual bool UpdateEdgeWeight(T source, T destination, long weight)
                 return false;
 
             // Edge exists, use only one triangle of the matrix
-            if (_adjacencyMatrix[srcIndex, dstIndex] != EMPTY_EDGE_SLOT)
+            if (!EMPTY_EDGE_SLOT.Equals(_adjacencyMatrix[srcIndex, dstIndex]))
                 _adjacencyMatrix[srcIndex, dstIndex] = weight;
             else
                 _adjacencyMatrix[dstIndex, srcIndex] = weight;
@@ -290,7 +290,7 @@ public override bool RemoveVertex(T vertex)
         /// <summary>
         /// Get edge object from source to destination.
         /// </summary>
-        public virtual WeightedEdge<T> GetEdge(T source, T destination)
+        public virtual WeightedEdge<T, W> GetEdge(T source, T destination)
         {
             // Get indices of vertices
             int srcIndex = _vertices.IndexOf(source);
@@ -302,13 +302,13 @@ public virtual WeightedEdge<T> GetEdge(T source, T destination)
             if (!_doesEdgeExist(srcIndex, dstIndex))
                 throw new Exception("Edge doesn't exist.");
 
-            return (new WeightedEdge<T>(source, destination, _getEdgeWeight(srcIndex, dstIndex)));
+            return (new WeightedEdge<T, W>(source, destination, _getEdgeWeight(srcIndex, dstIndex)));
         }
 
         /// <summary>
         /// Returns the edge weight from source to destination.
         /// </summary>
-        public virtual long GetEdgeWeight(T source, T destination)
+        public virtual W GetEdgeWeight(T source, T destination)
         {
             return GetEdge(source, destination).Weight;
         }
@@ -316,12 +316,12 @@ public virtual long GetEdgeWeight(T source, T destination)
         /// <summary>
         /// Returns the neighbours of a vertex as a dictionary of nodes-to-weights.
         /// </summary>
-        public virtual Dictionary<T, long> NeighboursMap(T vertex)
+        public virtual Dictionary<T, W> NeighboursMap(T vertex)
         {
             if (!HasVertex(vertex))
                 return null;
 
-            var neighbors = new Dictionary<T, long>();
+            var neighbors = new Dictionary<T, W>();
             int source = _vertices.IndexOf(vertex);
 
             // Check existence of vertex
@@ -370,7 +370,7 @@ public override void Clear()
             _edgesCount = 0;
             _verticesCount = 0;
             _vertices = new ArrayList<object>(_verticesCapacity);
-            _adjacencyMatrix = new long[_verticesCapacity, _verticesCapacity];
+            _adjacencyMatrix = new W[_verticesCapacity, _verticesCapacity];
             _adjacencyMatrix.Populate(rows: _verticesCapacity, columns: _verticesCapacity, defaultValue: EMPTY_EDGE_SLOT);
         }
     }
diff --git a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
index 20859241..2901442d 100644
--- a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
@@ -17,15 +17,15 @@
 
 namespace DataStructures.Graphs
 {
-    public class UndirectedWeightedSparseGraph<T> : IGraph<T>, IWeightedGraph<T> where T : IComparable<T>
+    public class UndirectedWeightedSparseGraph<T, W> : IGraph<T, W>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// INSTANCE VARIABLES
         /// </summary>
-        private const long EMPTY_EDGE_VALUE = 0;
+        private static readonly W EMPTY_EDGE_VALUE = default(W);
         protected virtual int _edgesCount { get; set; }
         protected virtual T _firstInsertedNode { get; set; }
-        protected virtual Dictionary<T, DLinkedList<WeightedEdge<T>>> _adjacencyList { get; set; }
+        protected virtual Dictionary<T, DLinkedList<WeightedEdge<T, W>>> _adjacencyList { get; set; }
 
 
         /// <summary>
@@ -36,20 +36,20 @@ public UndirectedWeightedSparseGraph() : this(10) { }
         public UndirectedWeightedSparseGraph(uint initialCapacity)
         {
             _edgesCount = 0;
-            _adjacencyList = new Dictionary<T, DLinkedList<WeightedEdge<T>>>((int)initialCapacity);
+            _adjacencyList = new Dictionary<T, DLinkedList<WeightedEdge<T, W>>>((int)initialCapacity);
         }
 
 
         /// <summary>
         /// Helper function. Returns edge object from source to destination, if exists; otherwise, null.
         /// </summary>
-        protected virtual WeightedEdge<T> _tryGetEdge(T source, T destination)
+        protected virtual WeightedEdge<T, W> _tryGetEdge(T source, T destination)
         {
             var success = false;
-            WeightedEdge<T> edge = null;
+            WeightedEdge<T, W> edge = null;
 
-            var sourceToDestinationPredicate = new Predicate<WeightedEdge<T>>((item) => item.Source.IsEqualTo<T>(source) && item.Destination.IsEqualTo<T>(destination));
-            var destinationToSourcePredicate = new Predicate<WeightedEdge<T>>((item) => item.Source.IsEqualTo<T>(destination) && item.Destination.IsEqualTo<T>(source));
+            var sourceToDestinationPredicate = new Predicate<WeightedEdge<T, W>>((item) => item.Source.IsEqualTo<T>(source) && item.Destination.IsEqualTo<T>(destination));
+            var destinationToSourcePredicate = new Predicate<WeightedEdge<T, W>>((item) => item.Source.IsEqualTo<T>(destination) && item.Destination.IsEqualTo<T>(source));
 
             if(_adjacencyList.ContainsKey(source))
                 success = _adjacencyList[source].TryFindFirst(sourceToDestinationPredicate, out edge);
@@ -73,7 +73,7 @@ protected virtual bool _doesEdgeExist(T source, T destination)
         /// Helper function. Gets the weight of a undirected edge.
         /// Presumes edge does already exist.
         /// </summary>
-        private long _getEdgeWeight(T source, T destination)
+        private W _getEdgeWeight(T source, T destination)
         {
             return _tryGetEdge(source, destination).Weight;
         }
@@ -124,17 +124,17 @@ public IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        IEnumerable<IEdge<T, W>> IGraph<T, W>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T, W>> IGraph<T, W>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T, W>> IGraph<T, W>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
@@ -143,7 +143,7 @@ IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         /// <summary>
         /// An enumerable collection of all weighted edges in Graph.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> Edges
+        public virtual IEnumerable<WeightedEdge<T, W>> Edges
         {
             get
             {
@@ -169,19 +169,19 @@ public virtual IEnumerable<WeightedEdge<T>> Edges
         /// <summary>
         /// Get all incoming weighted edges to a vertex
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex)
+        public virtual IEnumerable<WeightedEdge<T, W>> IncomingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
             
             foreach(var edge in _adjacencyList[vertex])
-                yield return (new WeightedEdge<T>(edge.Destination, edge.Source, edge.Weight));
+                yield return (new WeightedEdge<T, W>(edge.Destination, edge.Source, edge.Weight));
         }
 
         /// <summary>
         /// Get all outgoing weighted edges from a vertex.
         /// </summary>
-        public virtual IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex)
+        public virtual IEnumerable<WeightedEdge<T, W>> OutgoingEdges(T vertex)
         {
             if (!HasVertex(vertex))
                 throw new KeyNotFoundException("Vertex doesn't belong to graph.");
@@ -203,10 +203,10 @@ public bool AddEdge(T source, T destination)
         /// <summary>
         /// Connects two vertices together with a weight, in the direction: first->second.
         /// </summary>
-        public bool AddEdge(T source, T destination, long weight)
+        public bool AddEdge(T source, T destination, W weight)
         {
             // Check existence of nodes, the validity of the weight value, and the non-existence of edge
-            if (weight == EMPTY_EDGE_VALUE)
+            if (EMPTY_EDGE_VALUE.Equals(weight))
                 return false;
             if (!HasVertex(source) || !HasVertex(destination))
                 return false;
@@ -214,8 +214,8 @@ public bool AddEdge(T source, T destination, long weight)
                 return false;
 
             // Add edge from source to destination
-            var sourceDdge = new WeightedEdge<T>(source, destination, weight);
-            var destinationEdge = new WeightedEdge<T>(destination, source, weight);
+            var sourceDdge = new WeightedEdge<T, W>(source, destination, weight);
+            var destinationEdge = new WeightedEdge<T, W>(destination, source, weight);
 
             _adjacencyList[source].Append(sourceDdge);
             _adjacencyList[destination].Append(destinationEdge);
@@ -235,12 +235,12 @@ public virtual bool RemoveEdge(T source, T destination)
             if (!HasVertex(source) || !HasVertex(destination))
                 return false;
 
-            WeightedEdge<T> edge1, edge2;
+            WeightedEdge<T, W> edge1, edge2;
 
-            var sourceToDestinationPredicate = new Predicate<WeightedEdge<T>>((item) => item.Source.IsEqualTo<T>(source) && item.Destination.IsEqualTo<T>(destination));
+            var sourceToDestinationPredicate = new Predicate<WeightedEdge<T, W>>((item) => item.Source.IsEqualTo<T>(source) && item.Destination.IsEqualTo<T>(destination));
             _adjacencyList[source].TryFindFirst(sourceToDestinationPredicate, out edge1);
 
-            var destinationToSourcePredicate = new Predicate<WeightedEdge<T>>((item) => item.Source.IsEqualTo<T>(destination) && item.Destination.IsEqualTo<T>(source));
+            var destinationToSourcePredicate = new Predicate<WeightedEdge<T, W>>((item) => item.Source.IsEqualTo<T>(destination) && item.Destination.IsEqualTo<T>(source));
             _adjacencyList[destination].TryFindFirst(destinationToSourcePredicate, out edge2);
 
             // If edge doesn't exist, return false
@@ -261,10 +261,10 @@ public virtual bool RemoveEdge(T source, T destination)
             return true;
         }
 
-        public bool UpdateEdgeWeight(T source, T destination, long weight)
+        public bool UpdateEdgeWeight(T source, T destination, W weight)
         {
             // Check existence of vertices and validity of the weight value
-            if (weight == EMPTY_EDGE_VALUE)
+            if (EMPTY_EDGE_VALUE.Equals(weight))
                 return false;
             if (!HasVertex(source) || !HasVertex(destination))
                 return false;
@@ -300,7 +300,7 @@ public bool UpdateEdgeWeight(T source, T destination, long weight)
         /// <summary>
         /// Get edge object from source to destination.
         /// </summary>
-        public virtual WeightedEdge<T> GetEdge(T source, T destination)
+        public virtual WeightedEdge<T, W> GetEdge(T source, T destination)
         {
             if (!HasVertex(source) || !HasVertex(destination))
                 throw new KeyNotFoundException("Either one of the vertices or both of them don't exist.");
@@ -318,7 +318,7 @@ public virtual WeightedEdge<T> GetEdge(T source, T destination)
         /// <summary>
         /// Returns the edge weight from source to destination.
         /// </summary>
-        public virtual long GetEdgeWeight(T source, T destination)
+        public virtual W GetEdgeWeight(T source, T destination)
         {
             return GetEdge(source, destination).Weight;
         }
@@ -346,7 +346,7 @@ public virtual bool AddVertex(T vertex)
             if (_adjacencyList.Count == 0)
                 _firstInsertedNode = vertex;
 
-            _adjacencyList.Add(vertex, new DLinkedList<WeightedEdge<T>>());
+            _adjacencyList.Add(vertex, new DLinkedList<WeightedEdge<T, W>>());
 
             return true;
         }
@@ -414,13 +414,13 @@ public virtual DLinkedList<T> Neighbours(T vertex)
         /// <summary>
         /// Returns the neighbours of a vertex as a dictionary of nodes-to-weights.
         /// </summary>
-        public Dictionary<T, long> NeighboursMap(T vertex)
+        public Dictionary<T, W> NeighboursMap(T vertex)
         {
             if (!HasVertex(vertex))
                 return null;
 
             var neighbors = _adjacencyList[vertex];
-            var map = new Dictionary<T, long>(neighbors.Count);
+            var map = new Dictionary<T, W>(neighbors.Count);
 
             foreach (var adjacent in neighbors)
                 map.Add(adjacent.Destination, adjacent.Weight);
diff --git a/DataStructures/Graphs/UnweightedEdge.cs b/DataStructures/Graphs/UnweightedEdge.cs
index 8bffc61f..123026b4 100644
--- a/DataStructures/Graphs/UnweightedEdge.cs
+++ b/DataStructures/Graphs/UnweightedEdge.cs
@@ -53,7 +53,7 @@ public UnweightedEdge(TVertex src, TVertex dst)
 
 
         #region IComparable implementation
-        public int CompareTo(IEdge<TVertex> other)
+        public int CompareTo(IEdge<TVertex, Int64> other)
         {
             if (other == null)
                 return -1;
diff --git a/DataStructures/Graphs/WeightedEdge.cs b/DataStructures/Graphs/WeightedEdge.cs
index 8c2979bd..c20040a8 100644
--- a/DataStructures/Graphs/WeightedEdge.cs
+++ b/DataStructures/Graphs/WeightedEdge.cs
@@ -7,7 +7,9 @@ namespace DataStructures.Graphs
     /// <summary>
     /// The graph weighted edge class.
     /// </summary>
-    public class WeightedEdge<TVertex> : IEdge<TVertex> where TVertex : IComparable<TVertex>
+    public class WeightedEdge<TVertex, TWeight> : IEdge<TVertex, TWeight>
+        where TVertex : IComparable<TVertex>
+        where TWeight : IComparable<TWeight>
     {
         /// <summary>
         /// Gets or sets the source.
@@ -25,7 +27,7 @@ public class WeightedEdge<TVertex> : IEdge<TVertex> where TVertex : IComparable<
         /// Gets or sets the weight of edge.
         /// </summary>
         /// <value>The weight.</value>
-        public Int64 Weight { get; set; }
+        public TWeight Weight { get; set; }
 
         /// <summary>
         /// Gets a value indicating whether this edge is weighted.
@@ -39,7 +41,7 @@ public bool IsWeighted
         /// <summary>
         /// CONSTRUCTOR
         /// </summary>
-        public WeightedEdge(TVertex src, TVertex dst, Int64 weight)
+        public WeightedEdge(TVertex src, TVertex dst, TWeight weight)
         {
             Source = src;
             Destination = dst;
@@ -48,7 +50,7 @@ public WeightedEdge(TVertex src, TVertex dst, Int64 weight)
 
 
         #region IComparable implementation
-        public int CompareTo(IEdge<TVertex> other)
+        public int CompareTo(IEdge<TVertex, TWeight> other)
         {
             if (other == null)
                 return -1;

From 9ab1535130531cd702636e62fa004b5922439ec1 Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Wed, 8 Aug 2018 21:06:55 +0800
Subject: [PATCH 02/12] Add default weight type for IWeightedGraph.

---
 DataStructures/Graphs/IWeightedGraph.cs | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DataStructures/Graphs/IWeightedGraph.cs b/DataStructures/Graphs/IWeightedGraph.cs
index c994edb4..1f62d649 100644
--- a/DataStructures/Graphs/IWeightedGraph.cs
+++ b/DataStructures/Graphs/IWeightedGraph.cs
@@ -32,5 +32,7 @@ public interface IWeightedGraph<T, W> where T : IComparable<T> where W : ICompar
         /// </summary>
         System.Collections.Generic.Dictionary<T, W> NeighboursMap(T vertex);
     }
+
+    public interface IWeightedGraph<T> : IWeightedGraph<T, Int64> where T : IComparable<T> { }
 }
 

From b03600b0939d26aba445596c3469705a661fbd7d Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Thu, 9 Aug 2018 14:20:05 +0800
Subject: [PATCH 03/12] Add default WeightedEdge with long weights.

---
 DataStructures/Graphs/WeightedEdge.cs | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/DataStructures/Graphs/WeightedEdge.cs b/DataStructures/Graphs/WeightedEdge.cs
index c20040a8..c972d386 100644
--- a/DataStructures/Graphs/WeightedEdge.cs
+++ b/DataStructures/Graphs/WeightedEdge.cs
@@ -63,4 +63,11 @@ public int CompareTo(IEdge<TVertex, TWeight> other)
         }
         #endregion
     }
+
+    public class WeightedEdge<TVertex> : WeightedEdge<TVertex, Int64> where TVertex : IComparable<TVertex>
+    {
+        public WeightedEdge(TVertex src, TVertex dst, long weight) : base(src, dst, weight)
+        {
+        }
+    }
 }

From c358a40e0f261371ee33de516aac101ed01e9542 Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Thu, 9 Aug 2018 14:30:56 +0800
Subject: [PATCH 04/12] Add default weight type for all weighted graph classes.

---
 DataStructures/Graphs/DirectedWeightedDenseGraph.cs    | 2 +-
 DataStructures/Graphs/DirectedWeightedSparseGraph.cs   | 1 +
 DataStructures/Graphs/UndirectedWeightedDenseGraph.cs  | 1 +
 DataStructures/Graphs/UndirectedWeightedSparseGraph.cs | 2 ++
 4 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
index 521991e8..1d190781 100644
--- a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
@@ -357,5 +357,5 @@ public override void Clear()
 
     }
 
+    public class DirectedWeightedDenseGraph<T> : DirectedWeightedDenseGraph<T, Int64> where T : IComparable<T> { }
 }
-
diff --git a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
index 5c72cd9d..72f690b2 100644
--- a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
@@ -538,4 +538,5 @@ public virtual void Clear()
 
     }
 
+    public class DirectedWeightedSparseGraph<T> : DirectedWeightedSparseGraph<T, Int64> where T : IComparable<T> { }
 }
diff --git a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
index d3f6fb16..c9f43eb4 100644
--- a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
@@ -375,4 +375,5 @@ public override void Clear()
         }
     }
 
+    public class UndirectedWeightedDenseGraph<T> : UndirectedWeightedDenseGraph<T, Int64> where T : IComparable<T> { }
 }
diff --git a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
index 2901442d..cf86d93f 100644
--- a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
@@ -568,4 +568,6 @@ public virtual void Clear()
         }
     }
 
+
+    public class UndirectedWeightedSparseGraph<T> : UndirectedWeightedSparseGraph<T, Int64> where T : IComparable<T> { }
 }

From 1c08ff2c509c1efbd63248f7ab5008ae2fa43b4e Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Mon, 20 Aug 2018 20:17:37 +0800
Subject: [PATCH 05/12] Fix unit tests.

---
 DataStructures/Graphs/DirectedWeightedDenseGraph.cs         | 2 +-
 DataStructures/Graphs/DirectedWeightedSparseGraph.cs        | 2 +-
 DataStructures/Graphs/UndirectedWeightedDenseGraph.cs       | 2 +-
 DataStructures/Graphs/UndirectedWeightedSparseGraph.cs      | 2 +-
 UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs  | 2 +-
 UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
index 1d190781..b49c33dd 100644
--- a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
@@ -357,5 +357,5 @@ public override void Clear()
 
     }
 
-    public class DirectedWeightedDenseGraph<T> : DirectedWeightedDenseGraph<T, Int64> where T : IComparable<T> { }
+    public class DirectedWeightedDenseGraph<T> : DirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T> { }
 }
diff --git a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
index 72f690b2..ac3c67a5 100644
--- a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
@@ -538,5 +538,5 @@ public virtual void Clear()
 
     }
 
-    public class DirectedWeightedSparseGraph<T> : DirectedWeightedSparseGraph<T, Int64> where T : IComparable<T> { }
+    public class DirectedWeightedSparseGraph<T> : DirectedWeightedSparseGraph<T, Int64>, IGraph<T>, IWeightedGraph<T> where T : IComparable<T> { }
 }
diff --git a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
index c9f43eb4..da7026ab 100644
--- a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
@@ -375,5 +375,5 @@ public override void Clear()
         }
     }
 
-    public class UndirectedWeightedDenseGraph<T> : UndirectedWeightedDenseGraph<T, Int64> where T : IComparable<T> { }
+    public class UndirectedWeightedDenseGraph<T> : UndirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T> { }
 }
diff --git a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
index cf86d93f..e4baa2a2 100644
--- a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
@@ -569,5 +569,5 @@ public virtual void Clear()
     }
 
 
-    public class UndirectedWeightedSparseGraph<T> : UndirectedWeightedSparseGraph<T, Int64> where T : IComparable<T> { }
+    public class UndirectedWeightedSparseGraph<T> : UndirectedWeightedSparseGraph<T, Int64>, IGraph<T>, IWeightedGraph<T> where T : IComparable<T> { }
 }
diff --git a/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs b/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs
index b6ab8940..08c954ec 100644
--- a/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs
+++ b/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs
@@ -13,7 +13,7 @@ public static class GraphsBellmanFordShortestPaths
         public static void DoTest()
         {
             string[] V;
-            IEnumerable<WeightedEdge<string>> E;
+            IEnumerable<WeightedEdge<string, long>> E;
             DirectedWeightedSparseGraph<string> graph;
             BellmanFordShortestPaths<DirectedWeightedSparseGraph<string>, string> BellmanFord;
 
diff --git a/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs b/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs
index 2ee32add..70410405 100644
--- a/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs
+++ b/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs
@@ -44,7 +44,7 @@ public static void DoTest()
             Assert.True(status == true);
 
             // Get E
-            IEnumerable<WeightedEdge<string>> E = graph.Edges;
+            IEnumerable<WeightedEdge<string, long>> E = graph.Edges;
             Assert.True(graph.EdgesCount == 10, "Wrong Edges Count.");
 
             // PRINT THE GRAPH

From 01ce17d8262b9e6f2eb1b8e15885812017b9e113 Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Tue, 21 Aug 2018 01:32:30 +0800
Subject: [PATCH 06/12] Revert changes in unit tests.

---
 UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs  | 2 +-
 UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs b/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs
index 08c954ec..b6ab8940 100644
--- a/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs
+++ b/UnitTest/AlgorithmsTests/GraphsBellmanFordShortestPaths.cs
@@ -13,7 +13,7 @@ public static class GraphsBellmanFordShortestPaths
         public static void DoTest()
         {
             string[] V;
-            IEnumerable<WeightedEdge<string, long>> E;
+            IEnumerable<WeightedEdge<string>> E;
             DirectedWeightedSparseGraph<string> graph;
             BellmanFordShortestPaths<DirectedWeightedSparseGraph<string>, string> BellmanFord;
 
diff --git a/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs b/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs
index 70410405..2ee32add 100644
--- a/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs
+++ b/UnitTest/AlgorithmsTests/GraphsDijkstraShortestPathsTest.cs
@@ -44,7 +44,7 @@ public static void DoTest()
             Assert.True(status == true);
 
             // Get E
-            IEnumerable<WeightedEdge<string, long>> E = graph.Edges;
+            IEnumerable<WeightedEdge<string>> E = graph.Edges;
             Assert.True(graph.EdgesCount == 10, "Wrong Edges Count.");
 
             // PRINT THE GRAPH

From 912968d8db26aadddfbcc8a428c47176ad3c38ea Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Tue, 21 Aug 2018 01:38:42 +0800
Subject: [PATCH 07/12] Add backward compatibility code.

---
 DataStructures/Graphs/CliqueGraph.cs          | 19 +++++++++++++++----
 DataStructures/Graphs/DirectedDenseGraph.cs   | 16 +++++++++++++++-
 DataStructures/Graphs/DirectedSparseGraph.cs  | 15 +++++++++++++++
 .../Graphs/DirectedWeightedDenseGraph.cs      |  5 ++++-
 .../Graphs/DirectedWeightedSparseGraph.cs     | 18 +++++++++++++++++-
 DataStructures/Graphs/IGraph.cs               | 18 +++++++++++++++++-
 DataStructures/Graphs/IWeightedGraph.cs       |  8 +++++++-
 DataStructures/Graphs/UndirectedDenseGraph.cs | 15 +++++++++++++++
 .../Graphs/UndirectedSparseGraph.cs           | 15 +++++++++++++++
 .../Graphs/UndirectedWeightedDenseGraph.cs    |  7 +++++--
 .../Graphs/UndirectedWeightedSparseGraph.cs   | 17 ++++++++++++++++-
 DataStructures/Graphs/WeightedEdge.cs         | 17 +++++++++++++++--
 12 files changed, 156 insertions(+), 14 deletions(-)

diff --git a/DataStructures/Graphs/CliqueGraph.cs b/DataStructures/Graphs/CliqueGraph.cs
index 6f7f3db3..557ba17e 100644
--- a/DataStructures/Graphs/CliqueGraph.cs
+++ b/DataStructures/Graphs/CliqueGraph.cs
@@ -255,7 +255,7 @@ ISet<UnordererPair<T>> getPairs(ICollection<T> vertices)
         /// <summary>
         /// An enumerable collection of all graph edges.
         /// </summary>
-        public IEnumerable<IEdge<T, Int64>> Edges
+        public IEnumerable<IEdge<T>> Edges
         {
             get
             {
@@ -269,11 +269,13 @@ public IEnumerable<IEdge<T, Int64>> Edges
                 return returnEdges;
             }
         }
+        
+        IEnumerable<IEdge<T, long>> IGraph<T, long>.Edges => this.Edges;
 
         /// <summary>
         /// Get all incoming edges to vertex.
         /// </summary>
-        public IEnumerable<IEdge<T, Int64>> IncomingEdges(T vertex)
+        public IEnumerable<IEdge<T>> IncomingEdges(T vertex)
         {
             List<UnweightedEdge<T>> incomingEdges = new List<UnweightedEdge<T>>();
 
@@ -292,11 +294,16 @@ public IEnumerable<IEdge<T, Int64>> IncomingEdges(T vertex)
             return incomingEdges;
 
         }
+        
+        IEnumerable<IEdge<T, long>> IGraph<T, long>.IncomingEdges(T vertex)
+        {
+            return this.IncomingEdges(vertex);
+        }
 
         /// <summary>
         /// Get all outgoing edges from a vertex.
         /// </summary>
-        public IEnumerable<IEdge<T, Int64>> OutgoingEdges(T vertex)
+        public IEnumerable<IEdge<T>> OutgoingEdges(T vertex)
         {
             List<UnweightedEdge<T>> outgoingEdges = new List<UnweightedEdge<T>>();
 
@@ -315,6 +322,11 @@ public IEnumerable<IEdge<T, Int64>> OutgoingEdges(T vertex)
             return outgoingEdges;
         }
 
+        IEnumerable<IEdge<T, long>> IGraph<T, long>.OutgoingEdges(T vertex)
+        {
+            return this.OutgoingEdges(vertex);
+        }
+
         /// <summary>
         /// Connects two vertices together.
         /// </summary>
@@ -824,7 +836,6 @@ static V Pick<V>(IEnumerable<V> Set)
             enumerator.Dispose();
             return ret;
         }
-
     }
 
     internal class UnordererPair<T> : Tuple<T, T>, IEquatable<UnordererPair<T>> where T : IEquatable<T>
diff --git a/DataStructures/Graphs/DirectedDenseGraph.cs b/DataStructures/Graphs/DirectedDenseGraph.cs
index caea4be0..c7814795 100644
--- a/DataStructures/Graphs/DirectedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedDenseGraph.cs
@@ -102,21 +102,35 @@ public virtual IEnumerable<T> Vertices
         }
 
 
+        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        {
+            get { return this.Edges; }
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        {
+            return this.IncomingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
 
+        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
+        {
+            return this.OutgoingEdges(vertex);
+        }
 
         /// <summary>
         /// An enumerable collection of all directed unweighted edges in graph.
diff --git a/DataStructures/Graphs/DirectedSparseGraph.cs b/DataStructures/Graphs/DirectedSparseGraph.cs
index a55c6e88..07275eda 100644
--- a/DataStructures/Graphs/DirectedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedSparseGraph.cs
@@ -92,16 +92,31 @@ public virtual IEnumerable<T> Vertices
         }
 
 
+        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        {
+            get { return this.Edges; }
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        {
+            return this.IncomingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        {
+            return this.OutgoingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
diff --git a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
index b49c33dd..492f8db8 100644
--- a/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedDenseGraph.cs
@@ -357,5 +357,8 @@ public override void Clear()
 
     }
 
-    public class DirectedWeightedDenseGraph<T> : DirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T> { }
+    public class DirectedWeightedDenseGraph<T> : DirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T>
+    {
+        public new WeightedEdge<T> GetEdge(T source, T destination) => base.GetEdge(source, destination).ToSimpleEdge();
+    }
 }
diff --git a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
index ac3c67a5..07486774 100644
--- a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
@@ -13,6 +13,7 @@
 
 using System;
 using System.Collections.Generic;
+using System.Linq;
 using DataStructures.Common;
 using DataStructures.Lists;
 
@@ -538,5 +539,20 @@ public virtual void Clear()
 
     }
 
-    public class DirectedWeightedSparseGraph<T> : DirectedWeightedSparseGraph<T, Int64>, IGraph<T>, IWeightedGraph<T> where T : IComparable<T> { }
+    public class DirectedWeightedSparseGraph<T> : DirectedWeightedSparseGraph<T, Int64>, IGraph<T>, IWeightedGraph<T> where T : IComparable<T>
+    {
+        public new IEnumerable<WeightedEdge<T>> Edges => base.Edges.Select(edge => edge.ToSimpleEdge());
+
+        public new WeightedEdge<T> GetEdge(T source, T destination) => base.GetEdge(source, destination).ToSimpleEdge();
+
+        public new IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex) => base.IncomingEdges(vertex).Select(edge => edge.ToSimpleEdge());
+
+        public new IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex) => base.OutgoingEdges(vertex).Select(edge => edge.ToSimpleEdge());
+
+        IEnumerable<IEdge<T>> IGraph<T>.Edges => this.Edges;
+
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex) => this.IncomingEdges(vertex);
+
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex) => this.OutgoingEdges(vertex);
+    }
 }
diff --git a/DataStructures/Graphs/IGraph.cs b/DataStructures/Graphs/IGraph.cs
index aba12999..b38e4fb4 100644
--- a/DataStructures/Graphs/IGraph.cs
+++ b/DataStructures/Graphs/IGraph.cs
@@ -124,6 +124,22 @@ public interface IGraph<T, W> where T : IComparable<T>
         /// </summary>
         void Clear();
     }
+    
+    public interface IGraph<T> : IGraph<T, Int64> where T : IComparable<T>
+    {
+        /// <summary>
+        /// An enumerable collection of edges.
+        /// </summary>
+        new IEnumerable<IEdge<T>> Edges { get; }
+
+        /// <summary>
+        /// Get all incoming edges from vertex
+        /// </summary>
+        new IEnumerable<IEdge<T>> IncomingEdges(T vertex);
 
-    public interface IGraph<T> : IGraph<T, Int64> where T : IComparable<T> { }
+        /// <summary>
+        /// Get all outgoing edges from vertex
+        /// </summary>
+        new IEnumerable<IEdge<T>> OutgoingEdges(T vertex);
+    }
 }
diff --git a/DataStructures/Graphs/IWeightedGraph.cs b/DataStructures/Graphs/IWeightedGraph.cs
index 1f62d649..d4877f78 100644
--- a/DataStructures/Graphs/IWeightedGraph.cs
+++ b/DataStructures/Graphs/IWeightedGraph.cs
@@ -33,6 +33,12 @@ public interface IWeightedGraph<T, W> where T : IComparable<T> where W : ICompar
         System.Collections.Generic.Dictionary<T, W> NeighboursMap(T vertex);
     }
 
-    public interface IWeightedGraph<T> : IWeightedGraph<T, Int64> where T : IComparable<T> { }
+    public interface IWeightedGraph<T> : IWeightedGraph<T, Int64> where T : IComparable<T>
+    {
+        /// <summary>
+        /// Get edge object from source to destination.
+        /// </summary>
+        new WeightedEdge<T> GetEdge(T source, T destination);
+    }
 }
 
diff --git a/DataStructures/Graphs/UndirectedDenseGraph.cs b/DataStructures/Graphs/UndirectedDenseGraph.cs
index 55f7d212..a7751962 100644
--- a/DataStructures/Graphs/UndirectedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedDenseGraph.cs
@@ -108,16 +108,31 @@ public virtual IEnumerable<T> Vertices
         }
 
 
+        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        {
+            get { return this.Edges; }
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        {
+            return this.IncomingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        {
+            return this.OutgoingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
diff --git a/DataStructures/Graphs/UndirectedSparseGraph.cs b/DataStructures/Graphs/UndirectedSparseGraph.cs
index 06a50d9b..601f7fdd 100644
--- a/DataStructures/Graphs/UndirectedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedSparseGraph.cs
@@ -93,16 +93,31 @@ public virtual IEnumerable<T> Vertices
         }
 
 
+        IEnumerable<IEdge<T>> IGraph<T>.Edges
+        {
+            get { return this.Edges; }
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
         {
             get { return this.Edges; }
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
+        {
+            return this.IncomingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
+        {
+            return this.OutgoingEdges(vertex);
+        }
+
         IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
diff --git a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
index da7026ab..4f884746 100644
--- a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
@@ -374,6 +374,9 @@ public override void Clear()
             _adjacencyMatrix.Populate(rows: _verticesCapacity, columns: _verticesCapacity, defaultValue: EMPTY_EDGE_SLOT);
         }
     }
-
-    public class UndirectedWeightedDenseGraph<T> : UndirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T> { }
+    
+    public class UndirectedWeightedDenseGraph<T> : UndirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T>
+    {
+        public new WeightedEdge<T> GetEdge(T source, T destination) => base.GetEdge(source, destination).ToSimpleEdge();
+    }
 }
diff --git a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
index e4baa2a2..bd521673 100644
--- a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
@@ -12,6 +12,7 @@
 
 using System;
 using System.Collections.Generic;
+using System.Linq;
 using DataStructures.Common;
 using DataStructures.Lists;
 
@@ -567,7 +568,21 @@ public virtual void Clear()
             _adjacencyList.Clear();
         }
     }
+    
+    public class UndirectedWeightedSparseGraph<T> : UndirectedWeightedSparseGraph<T, Int64>, IGraph<T>, IWeightedGraph<T> where T : IComparable<T>
+    {
+        public new IEnumerable<WeightedEdge<T>> Edges => base.Edges.Select(edge => edge.ToSimpleEdge());
+
+        public new WeightedEdge<T> GetEdge(T source, T destination) => base.GetEdge(source, destination).ToSimpleEdge();
+
+        public new IEnumerable<WeightedEdge<T>> IncomingEdges(T vertex) => base.IncomingEdges(vertex).Select(edge => edge.ToSimpleEdge());
 
+        public new IEnumerable<WeightedEdge<T>> OutgoingEdges(T vertex) => base.OutgoingEdges(vertex).Select(edge => edge.ToSimpleEdge());
 
-    public class UndirectedWeightedSparseGraph<T> : UndirectedWeightedSparseGraph<T, Int64>, IGraph<T>, IWeightedGraph<T> where T : IComparable<T> { }
+        IEnumerable<IEdge<T>> IGraph<T>.Edges => this.Edges;
+
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex) => this.IncomingEdges(vertex);
+
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex) => this.OutgoingEdges(vertex);
+    }
 }
diff --git a/DataStructures/Graphs/WeightedEdge.cs b/DataStructures/Graphs/WeightedEdge.cs
index c972d386..4b4ab19d 100644
--- a/DataStructures/Graphs/WeightedEdge.cs
+++ b/DataStructures/Graphs/WeightedEdge.cs
@@ -63,11 +63,24 @@ public int CompareTo(IEdge<TVertex, TWeight> other)
         }
         #endregion
     }
-
-    public class WeightedEdge<TVertex> : WeightedEdge<TVertex, Int64> where TVertex : IComparable<TVertex>
+    
+    public class WeightedEdge<TVertex> : WeightedEdge<TVertex, Int64>, IEdge<TVertex> where TVertex : IComparable<TVertex>
     {
         public WeightedEdge(TVertex src, TVertex dst, long weight) : base(src, dst, weight)
         {
         }
+
+        public WeightedEdge(WeightedEdge<TVertex, Int64> edge) : base(edge.Source, edge.Destination, edge.Weight)
+        {
+        }
+    }
+
+    public static class WeightedEdgeExtension
+    {
+        public static WeightedEdge<TVertex> ToSimpleEdge<TVertex>(this WeightedEdge<TVertex, Int64> edge)
+            where TVertex : IComparable<TVertex>
+        {
+            return new WeightedEdge<TVertex>(edge.Source, edge.Destination, edge.Weight);
+        }
     }
 }

From 2a908aaa8b9249ad988e00ab99b1174052cb875a Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Tue, 21 Aug 2018 01:53:17 +0800
Subject: [PATCH 08/12] Fix Dijkstra unit test on arithmetic overflow.

---
 Algorithms/Graphs/DijkstraShortestPaths.cs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Algorithms/Graphs/DijkstraShortestPaths.cs b/Algorithms/Graphs/DijkstraShortestPaths.cs
index 516eb5bc..8a9e8a01 100644
--- a/Algorithms/Graphs/DijkstraShortestPaths.cs
+++ b/Algorithms/Graphs/DijkstraShortestPaths.cs
@@ -205,7 +205,7 @@ private bool _checkOptimalityConditions(TGraph graph, TVertex source)
                 {
                     var w = _nodesToIndices[edge.Key];
 
-                    if (_distances[v] + edge.Value < _distances[w])
+                    if (_distances[v] < _distances[w] - edge.Value)
                     {
                         Console.WriteLine("edge " + vertex + "-" + edge.Key + " is not relaxed");
                         return false;

From 19b69b176ce6a16d0dc27af4a814e079cb426d7b Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Fri, 26 Jul 2019 22:52:17 +0800
Subject: [PATCH 09/12] Fix DFS and BFS tests of UndirectedWeightedDenseGraph.

---
 .../GraphsUndirectedWeightedDenseGraphTest.cs | 24 ++++++++-----------
 1 file changed, 10 insertions(+), 14 deletions(-)

diff --git a/UnitTest/DataStructuresTests/GraphsUndirectedWeightedDenseGraphTest.cs b/UnitTest/DataStructuresTests/GraphsUndirectedWeightedDenseGraphTest.cs
index bbb0db4f..38c8e5ee 100644
--- a/UnitTest/DataStructuresTests/GraphsUndirectedWeightedDenseGraphTest.cs
+++ b/UnitTest/DataStructuresTests/GraphsUndirectedWeightedDenseGraphTest.cs
@@ -85,28 +85,26 @@ public static void DoTest()
             // BFS from A
             // Walk the graph using BFS from A:
             var bfsWalk = graph.BreadthFirstWalk("a");
-
-            // output: (s) (a) (x) (z) (d) (c) (f) (v)
-            // output: (s) (a) (x) (z) (d) (c) (f) (v)
-            Assert.True(bfsWalk.SequenceEqual(new[] { "s", "a", "x", "z", "d", "c", "f", "v" }));
+            // output: (a) (z) (s) (x) (d) (c) (f) (v)
+            Assert.True(bfsWalk.SequenceEqual(new[] { "a", "z", "s", "x", "d", "c", "f", "v" }));
 
             // DFS from A
             // Walk the graph using DFS from A:
             var dfsWalk = graph.DepthFirstWalk("a");
-            // output: (s) (a) (x) (z) (d) (c) (f) (v)
-            Assert.True(bfsWalk.SequenceEqual(new[] { "s", "a", "x", "z", "d", "c", "f", "v" }));
+            // output: (a) (x) (c) (v) (f) (d) (s) (z)
+            Assert.True(dfsWalk.SequenceEqual(new[] { "a", "x", "c", "v", "f", "d", "s", "z" }));
 
             // BFS from F
             // Walk the graph using BFS from F:
             bfsWalk = graph.BreadthFirstWalk("f");
-            // output: (s) (a) (x) (z) (d) (c) (f) (v)
-            Assert.True(bfsWalk.SequenceEqual(new[] { "s", "a", "x", "z", "d", "c", "f", "v" }));
+            // output: (f) (d) (c) (s) (x) (v) (a) (z)
+            Assert.True(bfsWalk.SequenceEqual(new[] { "f", "d", "c", "s", "x", "v", "a", "z" }));
 
             // DFS from F
             // Walk the graph using DFS from F:
             dfsWalk = graph.DepthFirstWalk("f");
-            // output: (s) (a) (x) (z) (d) (c) (f) (v)
-            Assert.True(bfsWalk.SequenceEqual(new[] { "s", "a", "x", "z", "d", "c", "f", "v" }));
+            // output: (f) (c) (v) (d) (x) (s) (a) (z)
+            Assert.True(dfsWalk.SequenceEqual(new[] { "f", "c", "v", "d", "x", "s", "a", "z" }));
 
 
             /********************************************************************/
@@ -131,10 +129,8 @@ public static void DoTest()
 
             // Walk the graph using DFS:
             dfsWalk = graph.DepthFirstWalk();
-            // output: (a) (b) (e) (d) (c) (f) 
-            Assert.True(bfsWalk.SequenceEqual(new[] { "a", "b", "e", "d", "c", "f" }));
-
-            Console.ReadLine();
+            // output: (a) (d) (e) (c) (f) (b) 
+            Assert.True(dfsWalk.SequenceEqual(new[] { "a", "d", "e", "c", "f", "b" }));
         }
 
     }

From 0e01698d3c5fb9474db95264c9ef56ea2af8bf8a Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Thu, 23 Jan 2020 15:38:44 +0800
Subject: [PATCH 10/12] Fix null pointer exception.

---
 DataStructures/Graphs/UndirectedWeightedDenseGraph.cs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
index 5ba64b86..964fc549 100644
--- a/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedDenseGraph.cs
@@ -347,6 +347,6 @@ public override void Clear()
 
     public class UndirectedWeightedDenseGraph<T> : UndirectedWeightedDenseGraph<T, Int64>, IWeightedGraph<T> where T : IComparable<T>
     {
-        public new WeightedEdge<T> GetEdge(T source, T destination) => base.GetEdge(source, destination).ToSimpleEdge();
+        public new WeightedEdge<T> GetEdge(T source, T destination) => base.GetEdge(source, destination)?.ToSimpleEdge();
     }
 }

From e030c7dbdc8a971fadd879d3e0a58ab3c21a5fec Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Thu, 23 Jan 2020 16:38:44 +0800
Subject: [PATCH 11/12] Remove unecessary custom weight support.

---
 Algorithms/Graphs/DijkstraShortestPaths.cs    | 18 ++++++++++--
 DataStructures/Graphs/CliqueGraph.cs          | 16 ++---------
 DataStructures/Graphs/DirectedDenseGraph.cs   | 15 ----------
 DataStructures/Graphs/DirectedSparseGraph.cs  | 15 ----------
 .../Graphs/DirectedWeightedSparseGraph.cs     |  8 +++---
 DataStructures/Graphs/IEdge.cs                | 11 +-------
 DataStructures/Graphs/IGraph.cs               | 28 ++++---------------
 DataStructures/Graphs/UndirectedDenseGraph.cs | 15 ----------
 .../Graphs/UndirectedSparseGraph.cs           | 15 ----------
 .../Graphs/UndirectedWeightedSparseGraph.cs   |  8 +++---
 DataStructures/Graphs/UnweightedEdge.cs       | 16 ++---------
 DataStructures/Graphs/WeightedEdge.cs         | 12 ++++----
 12 files changed, 41 insertions(+), 136 deletions(-)

diff --git a/Algorithms/Graphs/DijkstraShortestPaths.cs b/Algorithms/Graphs/DijkstraShortestPaths.cs
index c72f7719..1977ab72 100644
--- a/Algorithms/Graphs/DijkstraShortestPaths.cs
+++ b/Algorithms/Graphs/DijkstraShortestPaths.cs
@@ -27,6 +27,20 @@ public class DijkstraShortestPaths<TGraph, TVertex>
         private readonly TGraph _graph;
         private readonly TVertex _source;
 
+        private long GetEdgeWeight(IEdge<TVertex> edge)
+        {
+            // TODO: Change Dijkstra algorithm to support edge weights that are not Int64 compatible.
+            if (edge.IsWeighted)
+            {
+                var e = edge as WeightedEdge<TVertex>;
+                return e.Weight;
+            }
+            else
+            {
+                return 1;
+            }
+        }
+
         public DijkstraShortestPaths(TGraph graph, TVertex source)
         {
             if (graph == null)
@@ -38,7 +52,7 @@ public DijkstraShortestPaths(TGraph graph, TVertex source)
             if (!graph.HasVertex(source))
                 throw new ArgumentException("The source vertex doesn't belong to graph.");
 
-            if (graph.Edges.Any(edge => edge.Weight < 0))
+            if (graph.Edges.Any(edge => GetEdgeWeight(edge) < 0))
                 throw new ArgumentException("Negative edge weight detected.");
 
             _graph = graph;
@@ -62,7 +76,7 @@ private void _dijkstra()
                 foreach (var outgoingEdge in outgoingEdges)
                 {
                     var adjacentIndex = _nodesToIndices[outgoingEdge.Destination];
-                    var delta = _distances[currentVertexIndex] != Infinity ? _distances[currentVertexIndex] + outgoingEdge.Weight : Infinity;
+                    var delta = _distances[currentVertexIndex] != Infinity ? _distances[currentVertexIndex] + GetEdgeWeight(outgoingEdge) : Infinity;
 
                     if (delta < _distances[adjacentIndex])
                     {
diff --git a/DataStructures/Graphs/CliqueGraph.cs b/DataStructures/Graphs/CliqueGraph.cs
index 557ba17e..4707c976 100644
--- a/DataStructures/Graphs/CliqueGraph.cs
+++ b/DataStructures/Graphs/CliqueGraph.cs
@@ -269,8 +269,6 @@ public IEnumerable<IEdge<T>> Edges
                 return returnEdges;
             }
         }
-        
-        IEnumerable<IEdge<T, long>> IGraph<T, long>.Edges => this.Edges;
 
         /// <summary>
         /// Get all incoming edges to vertex.
@@ -294,11 +292,6 @@ public IEnumerable<IEdge<T>> IncomingEdges(T vertex)
             return incomingEdges;
 
         }
-        
-        IEnumerable<IEdge<T, long>> IGraph<T, long>.IncomingEdges(T vertex)
-        {
-            return this.IncomingEdges(vertex);
-        }
 
         /// <summary>
         /// Get all outgoing edges from a vertex.
@@ -322,11 +315,6 @@ public IEnumerable<IEdge<T>> OutgoingEdges(T vertex)
             return outgoingEdges;
         }
 
-        IEnumerable<IEdge<T, long>> IGraph<T, long>.OutgoingEdges(T vertex)
-        {
-            return this.OutgoingEdges(vertex);
-        }
-
         /// <summary>
         /// Connects two vertices together.
         /// </summary>
@@ -406,7 +394,7 @@ public void AddVertices(IEnumerable<T> collection)
         /// Adds a list of vertices to the graph.
         /// </summary>
         /// <param name="collection">Collection.</param>
-        void IGraph<T, Int64>.AddVertices(IList<T> collection)
+        void IGraph<T>.AddVertices(IList<T> collection)
         {
             AddVertices(collection);
         }
@@ -610,7 +598,7 @@ ICollection<UnordererPair<T>> getEdges()
         /// Returns the list of Vertices.
         /// </summary>
         /// <value>The vertices.</value>
-        IEnumerable<T> IGraph<T, Int64>.Vertices
+        IEnumerable<T> IGraph<T>.Vertices
         {
             get
             {
diff --git a/DataStructures/Graphs/DirectedDenseGraph.cs b/DataStructures/Graphs/DirectedDenseGraph.cs
index c7814795..14150a2a 100644
--- a/DataStructures/Graphs/DirectedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedDenseGraph.cs
@@ -107,31 +107,16 @@ IEnumerable<IEdge<T>> IGraph<T>.Edges
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
-        {
-            get { return this.Edges; }
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
-        {
-            return this.IncomingEdges(vertex);
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
-        {
-            return this.OutgoingEdges(vertex);
-        }
-
         /// <summary>
         /// An enumerable collection of all directed unweighted edges in graph.
         /// </summary>
diff --git a/DataStructures/Graphs/DirectedSparseGraph.cs b/DataStructures/Graphs/DirectedSparseGraph.cs
index 07275eda..e8ce7df9 100644
--- a/DataStructures/Graphs/DirectedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedSparseGraph.cs
@@ -97,31 +97,16 @@ IEnumerable<IEdge<T>> IGraph<T>.Edges
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
-        {
-            get { return this.Edges; }
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
-        {
-            return this.IncomingEdges(vertex);
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
-        {
-            return this.OutgoingEdges(vertex);
-        }
-
 
         /// <summary>
         /// An enumerable collection of all directed unweighted edges in graph.
diff --git a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
index 07486774..4222ac39 100644
--- a/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/DirectedWeightedSparseGraph.cs
@@ -19,7 +19,7 @@
 
 namespace DataStructures.Graphs
 {
-    public class DirectedWeightedSparseGraph<T, W> : IGraph<T, W>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
+    public class DirectedWeightedSparseGraph<T, W> : IGraph<T>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// INSTANCE VARIABLES
@@ -124,17 +124,17 @@ public IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T, W>> IGraph<T, W>.Edges
+        IEnumerable<IEdge<T>> IGraph<T>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T, W>> IGraph<T, W>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, W>> IGraph<T, W>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
diff --git a/DataStructures/Graphs/IEdge.cs b/DataStructures/Graphs/IEdge.cs
index ad9bb615..ca269042 100644
--- a/DataStructures/Graphs/IEdge.cs
+++ b/DataStructures/Graphs/IEdge.cs
@@ -5,7 +5,7 @@ namespace DataStructures.Graphs
     /// <summary>
     /// This interface should be implemented by all edges classes.
     /// </summary>
-    public interface IEdge<TVertex, TWeight> : IComparable<IEdge<TVertex, TWeight>> where TVertex : IComparable<TVertex>
+    public interface IEdge<TVertex> : IComparable<IEdge<TVertex>> where TVertex : IComparable<TVertex>
     {
         /// <summary>
         /// Gets a value indicating whether this edge is weighted.
@@ -24,15 +24,6 @@ public interface IEdge<TVertex, TWeight> : IComparable<IEdge<TVertex, TWeight>>
         /// </summary>
         /// <value>The destination.</value>
         TVertex Destination { get; set; }
-
-        /// <summary>
-        /// Gets or sets the weight of edge.
-        /// Unwighted edges can be thought of as edges of the same weight
-        /// </summary>
-        /// <value>The weight.</value>
-        TWeight Weight { get; set; }
     }
-
-    public interface IEdge<TVertex> : IEdge<TVertex, Int64> where TVertex : IComparable<TVertex> { }
 }
 
diff --git a/DataStructures/Graphs/IGraph.cs b/DataStructures/Graphs/IGraph.cs
index b38e4fb4..4b0e0a02 100644
--- a/DataStructures/Graphs/IGraph.cs
+++ b/DataStructures/Graphs/IGraph.cs
@@ -1,11 +1,11 @@
 using System;
 using System.Collections.Generic;
+
 using DataStructures.Lists;
-using System.Linq;
 
 namespace DataStructures.Graphs
 {
-    public interface IGraph<T, W> where T : IComparable<T>
+    public interface IGraph<T> where T : IComparable<T>
     {
         /// <summary>
         /// Returns true, if graph is directed; false otherwise.
@@ -35,17 +35,17 @@ public interface IGraph<T, W> where T : IComparable<T>
         /// <summary>
         /// An enumerable collection of edges.
         /// </summary>
-        IEnumerable<IEdge<T, W>> Edges { get; }
+        IEnumerable<IEdge<T>> Edges { get; }
 
         /// <summary>
         /// Get all incoming edges from vertex
         /// </summary>
-        IEnumerable<IEdge<T, W>> IncomingEdges(T vertex);
+        IEnumerable<IEdge<T>> IncomingEdges(T vertex);
 
         /// <summary>
         /// Get all outgoing edges from vertex
         /// </summary>
-        IEnumerable<IEdge<T, W>> OutgoingEdges(T vertex);
+        IEnumerable<IEdge<T>> OutgoingEdges(T vertex);
 
         /// <summary>
         /// Connects two vertices together.
@@ -124,22 +124,4 @@ public interface IGraph<T, W> where T : IComparable<T>
         /// </summary>
         void Clear();
     }
-    
-    public interface IGraph<T> : IGraph<T, Int64> where T : IComparable<T>
-    {
-        /// <summary>
-        /// An enumerable collection of edges.
-        /// </summary>
-        new IEnumerable<IEdge<T>> Edges { get; }
-
-        /// <summary>
-        /// Get all incoming edges from vertex
-        /// </summary>
-        new IEnumerable<IEdge<T>> IncomingEdges(T vertex);
-
-        /// <summary>
-        /// Get all outgoing edges from vertex
-        /// </summary>
-        new IEnumerable<IEdge<T>> OutgoingEdges(T vertex);
-    }
 }
diff --git a/DataStructures/Graphs/UndirectedDenseGraph.cs b/DataStructures/Graphs/UndirectedDenseGraph.cs
index aeb731bf..54de9f1c 100644
--- a/DataStructures/Graphs/UndirectedDenseGraph.cs
+++ b/DataStructures/Graphs/UndirectedDenseGraph.cs
@@ -113,31 +113,16 @@ IEnumerable<IEdge<T>> IGraph<T>.Edges
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
-        {
-            get { return this.Edges; }
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
-        {
-            return this.IncomingEdges(vertex);
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
-        {
-            return this.OutgoingEdges(vertex);
-        }
-
 
         /// <summary>
         /// An enumerable collection of edges.
diff --git a/DataStructures/Graphs/UndirectedSparseGraph.cs b/DataStructures/Graphs/UndirectedSparseGraph.cs
index 601f7fdd..3593c0ec 100644
--- a/DataStructures/Graphs/UndirectedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedSparseGraph.cs
@@ -98,31 +98,16 @@ IEnumerable<IEdge<T>> IGraph<T>.Edges
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.Edges
-        {
-            get { return this.Edges; }
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.IncomingEdges(T vertex)
-        {
-            return this.IncomingEdges(vertex);
-        }
-
         IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, Int64>> IGraph<T, Int64>.OutgoingEdges(T vertex)
-        {
-            return this.OutgoingEdges(vertex);
-        }
-
 
         /// <summary>
         /// An enumerable collection of all unweighted edges in Graph.
diff --git a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
index bd521673..af941571 100644
--- a/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
+++ b/DataStructures/Graphs/UndirectedWeightedSparseGraph.cs
@@ -18,7 +18,7 @@
 
 namespace DataStructures.Graphs
 {
-    public class UndirectedWeightedSparseGraph<T, W> : IGraph<T, W>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
+    public class UndirectedWeightedSparseGraph<T, W> : IGraph<T>, IWeightedGraph<T, W> where T : IComparable<T> where W : IComparable<W>
     {
         /// <summary>
         /// INSTANCE VARIABLES
@@ -125,17 +125,17 @@ public IEnumerable<T> Vertices
         }
 
 
-        IEnumerable<IEdge<T, W>> IGraph<T, W>.Edges
+        IEnumerable<IEdge<T>> IGraph<T>.Edges
         {
             get { return this.Edges; }
         }
 
-        IEnumerable<IEdge<T, W>> IGraph<T, W>.IncomingEdges(T vertex)
+        IEnumerable<IEdge<T>> IGraph<T>.IncomingEdges(T vertex)
         {
             return this.IncomingEdges(vertex);
         }
 
-        IEnumerable<IEdge<T, W>> IGraph<T, W>.OutgoingEdges(T vertex)
+        IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
         {
             return this.OutgoingEdges(vertex);
         }
diff --git a/DataStructures/Graphs/UnweightedEdge.cs b/DataStructures/Graphs/UnweightedEdge.cs
index 123026b4..65e1188e 100644
--- a/DataStructures/Graphs/UnweightedEdge.cs
+++ b/DataStructures/Graphs/UnweightedEdge.cs
@@ -9,8 +9,6 @@ namespace DataStructures.Graphs
     /// </summary>
     public class UnweightedEdge<TVertex> : IEdge<TVertex> where TVertex : IComparable<TVertex>
     {
-        private const int _edgeWeight = 0;
-
         /// <summary>
         /// Gets or sets the source vertex.
         /// </summary>
@@ -23,16 +21,6 @@ public class UnweightedEdge<TVertex> : IEdge<TVertex> where TVertex : IComparabl
         /// <value>The destination.</value>
         public TVertex Destination { get; set; }
 
-        /// <summary>
-        /// [PRIVATE MEMBER] Gets or sets the weight.
-        /// </summary>
-        /// <value>The weight.</value>
-        public Int64 Weight
-        {
-            get { throw new NotImplementedException("Unweighted edges don't have weights."); }
-            set { throw new NotImplementedException("Unweighted edges can't have weights."); }
-        }
-
         /// <summary>
         /// Gets a value indicating whether this edge is weighted.
         /// </summary>
@@ -53,9 +41,9 @@ public UnweightedEdge(TVertex src, TVertex dst)
 
 
         #region IComparable implementation
-        public int CompareTo(IEdge<TVertex, Int64> other)
+        public int CompareTo(IEdge<TVertex> other)
         {
-            if (other == null)
+            if (other == null || !(other is UnweightedEdge<TVertex>))
                 return -1;
 
             bool areNodesEqual = Source.IsEqualTo<TVertex>(other.Source) && Destination.IsEqualTo<TVertex>(other.Destination);
diff --git a/DataStructures/Graphs/WeightedEdge.cs b/DataStructures/Graphs/WeightedEdge.cs
index 428aa807..de45b9ee 100644
--- a/DataStructures/Graphs/WeightedEdge.cs
+++ b/DataStructures/Graphs/WeightedEdge.cs
@@ -7,7 +7,7 @@ namespace DataStructures.Graphs
     /// <summary>
     /// The graph weighted edge class.
     /// </summary>
-    public class WeightedEdge<TVertex, TWeight> : IEdge<TVertex, TWeight>
+    public class WeightedEdge<TVertex, TWeight> : IEdge<TVertex>
         where TVertex : IComparable<TVertex>
         where TWeight : IComparable<TWeight>
     {
@@ -49,16 +49,18 @@ public WeightedEdge(TVertex src, TVertex dst, TWeight weight)
 
 
         #region IComparable implementation
-        public int CompareTo(IEdge<TVertex, TWeight> other)
+        public int CompareTo(IEdge<TVertex> other)
         {
-            if (other == null)
+            if (other == null || !(other is WeightedEdge<TVertex, TWeight>))
                 return -1;
-            
+
             bool areNodesEqual = Source.IsEqualTo<TVertex>(other.Source) && Destination.IsEqualTo<TVertex>(other.Destination);
 
             if (!areNodesEqual)
                 return -1;
-            return Weight.CompareTo(other.Weight);
+
+            var o = other as WeightedEdge<TVertex, TWeight>;
+            return Weight.CompareTo(o.Weight);
         }
         #endregion
     }

From 71077caca0db64c6aa7e2ea58b404bf800e50373 Mon Sep 17 00:00:00 2001
From: Mengyu Zhou <mezho@microsoft.com>
Date: Thu, 23 Jan 2020 16:45:19 +0800
Subject: [PATCH 12/12] Revert blank line change.

---
 DataStructures/Graphs/DirectedDenseGraph.cs | 1 +
 1 file changed, 1 insertion(+)

diff --git a/DataStructures/Graphs/DirectedDenseGraph.cs b/DataStructures/Graphs/DirectedDenseGraph.cs
index 14150a2a..264dff1c 100644
--- a/DataStructures/Graphs/DirectedDenseGraph.cs
+++ b/DataStructures/Graphs/DirectedDenseGraph.cs
@@ -117,6 +117,7 @@ IEnumerable<IEdge<T>> IGraph<T>.OutgoingEdges(T vertex)
             return this.OutgoingEdges(vertex);
         }
 
+
         /// <summary>
         /// An enumerable collection of all directed unweighted edges in graph.
         /// </summary>