How to get max flow for every possible source/sink node pair using JUNG's Edmonds Karp?

Question

I have some simple Java/JUNG code that creates a directed graph, adds some edges with weights and capacity values, and runs a max flow analysis from the source node to sink node.

If you have: A --- (capacity 2) -----> B ---- (capacity 5)----> C and want to find max flow from A->C, it will be 2.

import edu.uci.ics.jung.algorithms.flows.EdmondsKarpMaxFlow;
import edu.uci.ics.jung.graph.DirectedSparseMultigraph;
import edu.uci.ics.jung.graph.util.EdgeType;
import org.apache.commons.collections15.Factory;
import org.apache.commons.collections15.Transformer;

import java.util.HashMap;
import java.util.Map;

public class stack {
    static int edgeCount = 0;

    static class MyNode {
        int id;
        public MyNode(int id) {
            this.id = id;
        }
        public String toString() {
            return "V"+id;
        }
    }

    static class MyLink {

        double capacity;
        double weight;
        int id;

        public MyLink(double weight, double capacity) {
            this.id = edgeCount++;
            this.weight = weight;
            this.capacity = capacity;
        }
        public String toString() {
            return "E"+id;
        }

    }
    public static void main(String[] args){
        DirectedSparseMultigraph<MyNode, MyLink> g = new DirectedSparseMultigraph<MyNode, MyLink>();

        Transformer<MyLink, Double> capTransformer = new Transformer<MyLink, Double>(){
            public Double transform(MyLink link) {
                return link.capacity;
            }
        };

        Map<MyLink, Double> edgeFlowMap = new HashMap<MyLink, Double>();
        // This Factory produces new edges for use by the algorithm
        Factory<MyLink> edgeFactory = new Factory<MyLink>() {
            public MyLink create() {
                return new MyLink(1.0, 1.0);
            }
        };

        // Create some MyNode objects to use as vertices
        MyNode n1 = new MyNode(1);
        MyNode n2 = new MyNode(2);
        MyNode n3 = new MyNode(3);
        MyNode n4 = new MyNode(4);
        MyNode n5 = new MyNode(5);
        MyNode n6 = new MyNode(6);
        MyNode n7 = new MyNode(7);
        // Add some directed edges along with the vertices to the graph
        g.addEdge(new MyLink(2.0, 48),n1, n2, EdgeType.DIRECTED);
        g.addEdge(new MyLink(2.0, 58),n2, n3, EdgeType.DIRECTED);
        g.addEdge(new MyLink(3.0, 192), n3, n5, EdgeType.DIRECTED);
        g.addEdge(new MyLink(2.0, 48), n5, n4, EdgeType.DIRECTED);
        g.addEdge(new MyLink(2.0, 20), n6, n1, EdgeType.DIRECTED);
        g.addEdge(new MyLink(8, 24), n7, n4, EdgeType.DIRECTED);

        System.out.println("RUNNING EDMONDS KARP MAX FLOW FOR SOURCE " + n1.toString() + " TO SINK " + n2.toString());
        EdmondsKarpMaxFlow<MyNode, MyLink> edk = new EdmondsKarpMaxFlow(g, n1, n2, capTransformer, edgeFlowMap, edgeFactory);
        edk.evaluate();
        System.out.println("The max flow is: " + edk.getMaxFlow());
    }
}

Running this will output:

RUNNING EDMONDS KARP MAX FLOW FOR SOURCE V1 TO SINK V2 The max flow is: 48

How can write an algorithm to make it run on every possible pair of source and sinks so I can see max flow of all paths in the graph? Completely new to this stuff so anything helps!

Answer 1

Just run the algorithm for every pair of nodes. There is no known algorithm that is more efficient for directed graphs: All pair Maximum Flow