public static int EdmondsKarp(IGraph graph, int source, int target)
{
int maxFlow = 0;
//create flow graph
MatrixGraph flow = new MatrixGraph(graph.VerticesCount, true, graph.GetEdges());
foreach (Edge edge in flow.GetEdges())
{
flow.UpdateEdgeWeight(edge.From, edge.To, -edge.Weight);
}
//create residual graph
MatrixGraph residual = new MatrixGraph(graph.VerticesCount, true, graph.GetEdges());
while (true)
{
List <Edge> augmentingPath = BFS(residual, source, target);
if (augmentingPath == null)
{
return(maxFlow);
}
int minWeight = int.MaxValue;
foreach (Edge edge in augmentingPath)
{
if (edge.Weight < minWeight)
{
minWeight = edge.Weight;
}
}
maxFlow += minWeight;
//uptade residual and flow graph
foreach (Edge edge in augmentingPath)
{
if (residual.DoesEdgeExist(edge.From, edge.To))
{
residual.UpdateEdgeWeight(edge.From, edge.To, -minWeight);
if (residual.GetEdgeWeight(edge.From, edge.To) == 0)
{
residual.DeleteEdge(edge.From, edge.To);
}
}
if (!residual.DoesEdgeExist(edge.To, edge.From))
{
residual.AddEdge(new Edge(edge.To, edge.From));
}
residual.UpdateEdgeWeight(edge.To, edge.From, minWeight);
flow.UpdateEdgeWeight(edge.From, edge.To, minWeight);
flow.UpdateEdgeWeight(edge.To, edge.From, -minWeight);
}
}
}
public static int ChceckConnectivity(IGraph graph)
{
int connectivity = 0;
if (!Algorithms.isConnected(graph))
{
return(connectivity);
}
//create flow network
MatrixGraph flowNetworkGraph = new MatrixGraph(graph.VerticesCount, true);
foreach (Edge edge in graph.GetEdges())
{
flowNetworkGraph.AddEdge(new Edge(edge.From, edge.To, 1));
flowNetworkGraph.AddEdge(new Edge(edge.To, edge.From, 1));
}
//pick random vertex
Random rand = new Random();
int source = rand.Next((int)flowNetworkGraph.VerticesCount);
int minMaxFlow = int.MaxValue;
for (int target = 0; target < flowNetworkGraph.VerticesCount; target++)
{
if (target == source)
{
continue;
}
//find max flow between s and t
int maxFlow = Algorithms.EdmondsKarp(flowNetworkGraph, source, target);
if (maxFlow < minMaxFlow)
{
minMaxFlow = maxFlow;
}
}
connectivity = minMaxFlow;
return(connectivity);
}
