/// <summary>
/// Generate graph assuming a simple, undirected, and symmetric adjacency matrix
/// </summary>
/// <param name="adjacencyMatrix"></param>
/// <returns></returns>
public static Graph <int> GenerateGraphForAdjacencyMatrix(int[,] adjacencyMatrix)
{
int length = adjacencyMatrix.GetLength(0);
var G = new Graph <int>();
int maxDegree = adjacencyMatrix.GetLength(0) - 1;
for (int i = 0; i < length; i++)
{
G.AddNode(new GraphNode <int>(i, maxDegree));
}
for (int i = 0; i < length; i++)
{
for (int j = 0; j < length; j++)
{
if (adjacencyMatrix[i, j] != 0)
{
G.TotalEdges++;
IGraphNode <int> .AddMutualNeighbor(G.graphStructure[i], G.graphStructure[j]);
}
}
}
return(G);
}
/// <summary>
/// Generate a graph that matches the given degree sequence. Returns null if unable to actualize.
/// </summary>
/// <param name="degreeSequence"></param>
/// <returns></returns>
public static Graph <int> GenerateGraphForDegreeSequence(int[] degreeSequence)
{
var degreeSequenceList = new List <DegreeSequenceData>(degreeSequence.Length);
int sumDegreeSequence = 0;
var G = new Graph <int>();
for (int i = 0; i < degreeSequence.Length; i++)
{
var node = new GraphNode <int>(i);
sumDegreeSequence += degreeSequence[i];
degreeSequenceList.Add(new DegreeSequenceData(node, degreeSequence[i]));
G.AddNode(node);
}
//By handshaking lemma
G.TotalEdges = sumDegreeSequence / 2;
while (true)
{
//sort the degree sequence from greatest to least degree value
//if multiple have the same degree value, pick the smaller vertex
degreeSequenceList.Sort((x, y) => x == y ? x.Vertex.GetValue().CompareTo(y.Vertex.GetValue()) : y.DegreeValue.CompareTo(x.DegreeValue));
var maxDegreeData = degreeSequenceList[0];
//get the maximum degree vertex
int maxDegree = maxDegreeData.DegreeValue;
//if the maximum degree vertex is 0, we can terminate the algorithm
if (maxDegree == 0)
{
return(G);
}
//assign its degree to 0, as we will assign edges to use up all its degrees
degreeSequenceList[0].DegreeValue = 0;
//not enough nodes remain to add neighbors to
if (maxDegree >= degreeSequence.Length)
{
return(null);
}
//assign a connected to the next maxDegree vertices, and decrement each degree value by 1
for (int i = 1; i <= maxDegree; i++)
{
degreeSequenceList[i].DegreeValue--;
//the neighbor node cannot be assigned, and therefore this degree sequence is not possible
if (degreeSequenceList[i].DegreeValue < 0)
{
return(null);
}
//assign the vertex to each neighbor
IGraphNode <int> .AddMutualNeighbor(maxDegreeData.Vertex, degreeSequenceList[i].Vertex);
}
}
}
public static List <Graph <int> > GenerateNonIsomorphicGraphsOfOrder(int order)
{
var nonIsomGraphs = new List <Graph <int> >();
var emptyGraph = EmptyGraph(order);
nonIsomGraphs.Add(emptyGraph);
var generationQueue = new Queue <Graph <int> >(order ^ (order - 1));
generationQueue.Enqueue(emptyGraph);
while (!generationQueue.IsEmpty())
{
var front = generationQueue.Dequeue();
//try adding an edge...
for (int i = 0; i < order; i++)
{
var node1 = front.graphStructure[i];
//find a missing edge
for (int j = i + 1; j < order; j++)
{
var node2 = front.graphStructure[j];
if (!node1.GetNeighbors().Contains(node2))
{
//spawn a clone
var clone = front.Clone();
IGraphNode <int> .AddMutualNeighbor(clone.graphStructure[i], clone.graphStructure[j]);
clone.TotalEdges++;
bool graph_already_generated = false;
foreach (var existing_graph in nonIsomGraphs)
{
if (Graph <int> .CheckGraphIsomorphism(clone, existing_graph))
{
graph_already_generated = true;
break;
}
}
if (!graph_already_generated)
{
nonIsomGraphs.Add(clone);
generationQueue.Enqueue(clone);
}
}
}
}
}
return(nonIsomGraphs);
}
/// <summary>
/// Creates a tree that has the given prufer encoding
/// </summary>
/// <param name="prufer"></param>
/// <returns></returns>
public static Tree <int> PruferEncodingToTree(int[] prufer)
{
var T = new Tree <int>();
var labeling = new Dictionary <int, GraphNode <int> >();
int n = 2 + prufer.Length;
for (int i = 1; i <= n; i++)
{
var node = new GraphNode <int>(i);
labeling.Add(i, node);
T.AddNode(node);
}
//count the number of times a label appears in the encoding
var pruferCount = new int[n];
foreach (var num in prufer)
{
//increase the number of times this label appears
pruferCount[num - 1]++;
}
GraphNode <int> prufer_node = null;
for (int prufer_index = 0; prufer_index < prufer.Length; prufer_index++)
{
for (int i = 1; i <= n; i++)
{
if (pruferCount[i - 1] == 0)
{
var leaf_node = labeling[i];
var neighbor_index = prufer[prufer_index];
prufer_node = labeling[neighbor_index];
IGraphNode <int> .AddMutualNeighbor(leaf_node, prufer_node);
//assigned prufer for the current label
pruferCount[i - 1] = -1;
//decrement prufer count for neighbor label
pruferCount[neighbor_index - 1]--;
break;
}
}
}
//assign the last vertex to the last prufer node
if (prufer_node != null)
{
IGraphNode <int> .AddMutualNeighbor(prufer_node, labeling[n]);
}
return(T);
}
public static Graph <int> GenerateCompleteBipartiteGraph(int n1, int n2)
{
int totalNodes = n1 + n2;
var G = new Graph <int>(totalNodes);
for (int i = 0; i < totalNodes; i++)
{
G.AddNode(new GraphNode <int>(i));
}
for (int i = 0; i < n1; i++)
{
for (int j = 0; j < n2; j++)
{
IGraphNode <int> .AddMutualNeighbor(G.graphStructure[i], G.graphStructure[n1 + j]);
}
}
G.TotalEdges = n1 * n2;
return(G);
}
static void MakeGraph()
{
//Create the vertex set
var A = new GraphNode <char>('A');
var B = new GraphNode <char>('B');
var C = new GraphNode <char>('C');
var D = new GraphNode <char>('D');
var E = new GraphNode <char>('E');
var F = new GraphNode <char>('F');
var G = new GraphNode <char>('G');
//Create the edge set
A.AddNeighbor(D);
B.AddNeighbor(G);
C.AddNeighbor(E);
D.AddNeighbor(B);
D.AddNeighbor(C);
F.AddNeighbor(E);
G.AddNeighbor(A);
G.AddNeighbor(F);
IGraphNode <char> .AddMutualNeighbor(A, B);
GraphNode <char>[] nodes = { A, B, C, D, E, F, G };
Graph <char> a_graph = new Graph <char>(nodes);
foreach (var node1 in nodes)
{
foreach (var node2 in nodes)
{
if (node1 == node2)
{
continue; //this is not a very interesting case...
}
Console.WriteLine("Does a path exist from {0} to {1}?\n", node1.GetValue(), node2.GetValue());
var path = a_graph.RunDFS(node1, node2);
//another way to call this function and run DFS
//var path = a_graph.RunSearch(new Stack<NodePath<char>>(), node1, node2);
if (path == null)
{
Console.WriteLine("\tNope :(");
}
else
{
Console.WriteLine("Using backtracking, the path is...");
//use a stack to figure out the order to take
var reverse_backtracking = new Stack <NodePath <char> >();
while (path != null)
{
reverse_backtracking.Push(path);
Console.Write("{0}", path.Node.GetValue());
path = path.Parent;
if (path != null)
{
Console.Write(" <- ");
}
}
Console.WriteLine("\n\tUsing a stack, the path in-order is ");
while (!reverse_backtracking.IsEmpty())
{
var top = reverse_backtracking.Pop();
Console.Write("{0}", top.Node.GetValue());
if (reverse_backtracking.Count > 0)
{
Console.Write(" -> ");
}
}
Console.WriteLine("\n-------------------------------\n");
}
}
}
}
private static void IsIsomorphic()
{
var a1 = new GraphNode <int>(1);
var b1 = new GraphNode <int>(2);
var c1 = new GraphNode <int>(3);
var d1 = new GraphNode <int>(4);
var e1 = new GraphNode <int>(5);
var f1 = new GraphNode <int>(6);
IGraphNode <int> .AddMutualNeighbor(a1, b1);
IGraphNode <int> .AddMutualNeighbor(b1, c1);
IGraphNode <int> .AddMutualNeighbor(b1, d1);
IGraphNode <int> .AddMutualNeighbor(c1, d1);
IGraphNode <int> .AddMutualNeighbor(d1, e1);
IGraphNode <int> .AddMutualNeighbor(e1, f1);
var G1 = new Graph <int>(a1, b1, c1, d1, e1, f1);
var a2 = new GraphNode <int>(1);
var b2 = new GraphNode <int>(2);
var c2 = new GraphNode <int>(3);
var d2 = new GraphNode <int>(4);
var e2 = new GraphNode <int>(5);
var f2 = new GraphNode <int>(6);
IGraphNode <int> .AddMutualNeighbor(a2, b2);
IGraphNode <int> .AddMutualNeighbor(b2, c2);
IGraphNode <int> .AddMutualNeighbor(c2, d2);
IGraphNode <int> .AddMutualNeighbor(c2, d2);
IGraphNode <int> .AddMutualNeighbor(d2, e2);
IGraphNode <int> .AddMutualNeighbor(e2, f2);
var G2 = new Graph <int>(a2, b2, c2, d2, e2, f2);
Graph <int> .CheckGraphIsomorphism(G1, G2);
/*
* var a1 = new GraphNode<int>(1);
* var b1 = new GraphNode<int>(2);
* var c1 = new GraphNode<int>(3);
* var d1 = new GraphNode<int>(4);
* var e1 = new GraphNode<int>(5);
* var f1 = new GraphNode<int>(6);
*
* IGraphNode<int>.AddMutualNeighbor(a1, b1);
* IGraphNode<int>.AddMutualNeighbor(b1, f1);
* IGraphNode<int>.AddMutualNeighbor(b1, c1);
* IGraphNode<int>.AddMutualNeighbor(c1, d1);
* IGraphNode<int>.AddMutualNeighbor(d1, e1);
* var G1 = new Graph<int>(a1, b1, c1, d1, e1, f1);
*
* var a2 = new GraphNode<int>(1);
* var b2 = new GraphNode<int>(2);
* var c2 = new GraphNode<int>(3);
* var d2 = new GraphNode<int>(4);
* var e2 = new GraphNode<int>(5);
* var f2 = new GraphNode<int>(6);
*
* IGraphNode<int>.AddMutualNeighbor(a2, b2);
* IGraphNode<int>.AddMutualNeighbor(b2, c2);
* IGraphNode<int>.AddMutualNeighbor(b2, f2);
* IGraphNode<int>.AddMutualNeighbor(c2, d2);
* IGraphNode<int>.AddMutualNeighbor(d2, e2);
* var G2 = new Graph<int>(f2, e2, d2, c2, b2, a2);
*
* Graph<int>.CheckGraphIsomorphism(G1, G2);
*
* Console.WriteLine("\n----------------------------------------------\n");
*
* int numberVertices = 4;
*
* var g3_adj = new int[numberVertices, numberVertices];
* g3_adj[0, 1] = 1;
* g3_adj[1, 2] = 1;
* g3_adj[1, 3] = 1;
* g3_adj[2, 3] = 1;
*
* var G3 = Graph<int>.GenerateGraphForAdjacencyMatrix(g3_adj, true);
*
* var g4_adj = new int[numberVertices, numberVertices];
* g4_adj[0, 1] = 1;
* g4_adj[0, 2] = 1;
* g4_adj[0, 3] = 1;
* g4_adj[2, 3] = 1;
*
* var G4 = Graph<int>.GenerateGraphForAdjacencyMatrix(g4_adj, true);
*
* Graph<int>.CheckGraphIsomorphism(G3, G4);
*
* Console.WriteLine("\n----------------------------------------------\n");
*
* numberVertices = 7;
*
* var g5_adj = new int[numberVertices, numberVertices];
* g5_adj[0, 1] = 1;
* g5_adj[1, 2] = 1;
* g5_adj[1, 3] = 1;
* g5_adj[2, 3] = 1;
* g5_adj[4, 5] = 1;
*
* var G5 = Graph<int>.GenerateGraphForAdjacencyMatrix(g5_adj, true);
*
* var g6_adj = new int[numberVertices, numberVertices];
* g6_adj[0, 1] = 1;
* g6_adj[0, 2] = 1;
* g6_adj[0, 3] = 1;
* g6_adj[2, 3] = 1;
* g6_adj[5, 6] = 1;
*
* var G6 = Graph<int>.GenerateGraphForAdjacencyMatrix(g6_adj, true);
*
* Graph<int>.CheckGraphIsomorphism(G5, G6);
*/
/* THIS IS AN ISOM TEST
* var adj1 = new int[5, 5];
* adj1[0, 1] = 1;
* adj1[0, 2] = 1;
* adj1[3, 4] = 1;
*
* var adj2 = new int[5, 5];
* adj2[0, 1] = 1;
* adj2[2, 3] = 1;
* adj2[2, 4] = 1;
*
* var g1 = Graph<int>.GenerateGraphForAdjacencyMatrix(adj1);
* var g2 = Graph<int>.GenerateGraphForAdjacencyMatrix(adj2);
*
* bool result = Graph<int>.CheckGraphIsomorphism(g1, g2);
*/
}
