How to determine if two nodes are connected?

Question

I\'m concerned that this might be working on an NP-Complete problem. I\'m hoping someone can give me an answer as to whether it is or not. And I\'m looking for more of an an

Answer 1

Any graph shortest path algorithm will be overkill if all you need is to find if a node is connected to another. A good Java library that accomplishes that is JGraphT. It's usage is quite simple, here's an example of an Integer graph:

public void loadGraph() {
    // first we create a new undirected graph of Integers
    UndirectedGraph graph = new SimpleGraph<>(DefaultEdge.class);

    // then we add some nodes
    graph.addVertex(1);
    graph.addVertex(2);
    graph.addVertex(3);
    graph.addVertex(4);
    graph.addVertex(5);
    graph.addVertex(6);
    graph.addVertex(7);
    graph.addVertex(8);
    graph.addVertex(9);
    graph.addVertex(10);
    graph.addVertex(11);
    graph.addVertex(12);
    graph.addVertex(13);
    graph.addVertex(14);
    graph.addVertex(15);
    graph.addVertex(16);

    // then we connect the nodes
    graph.addEdge(1, 2);
    graph.addEdge(2, 3);
    graph.addEdge(3, 4);
    graph.addEdge(3, 5);
    graph.addEdge(5, 6);
    graph.addEdge(6, 7);
    graph.addEdge(7, 8);
    graph.addEdge(8, 9);
    graph.addEdge(9, 10);
    graph.addEdge(10, 11);
    graph.addEdge(11, 12);
    graph.addEdge(13, 14);
    graph.addEdge(14, 15);
    graph.addEdge(15, 16);

    // finally we use ConnectivityInspector to check nodes connectivity
    ConnectivityInspector inspector = new ConnectivityInspector<>(graph);

    debug(inspector, 1, 2);
    debug(inspector, 1, 4);
    debug(inspector, 1, 3);
    debug(inspector, 1, 12);
    debug(inspector, 16, 5);
}

private void debug(ConnectivityInspector inspector, Integer n1, Integer n2) {
    System.out.println(String.format("are [%s] and [%s] connected? [%s]", n1, n2, inspector.pathExists(n1, n2)));
}

This lib also offers all the shortest paths algorithms as well.