Storing Edge Data in Adjacency List?

Question

I'm trying to create a simple directed graph data structure backed by a Hashtable which looks like this:

private Hashtable<V, List<Edge<V, K>>> adjacencyTable;

Where V is the vertex type and K is the data stored in an edge. The Edge class simply stores a reference to the two vertices it lies between as well as some object of type K . So...

1 | (1, 2, data_1), (1, 3, data_2)
2 | (2, 3, data_3)
3 | (3, 1, data_4)

So in order to do something simple like removeVertex(3) , I have to loop through all the edges for each vertex, check if their to property is equal to the vertex I'm trying to remove, and then delete them. Is there a better way to implement something like this?

Answer 1

Yes you're right this is an awkward choice. Consider instead using

Map<V, Map<V, K>> adjacencies = new Hashmap<>();

The nodes adjacent to p are adjacencies.get(p).keyset() , and the data for edge p->q is adjacencies.get(p).get(q) .

Removing vertex r is bound to be a tricky operation because you need to remove the both in- and out-edges of r . However you can make it quick by maintaining a parallel "reverse adjacency" list.

Map<V, Set<V>> reverseAdjacencies = new Hashmap<>();

Every time you add an adjacency p->q with something like:

Map<V, K> edgesFromP = adjacencies.get();
if (edgesFromP == null) {
  edgesFromP = new HashMap<>();
  adjacencies.put(p, edgesFromP);
}
edgesFromP.put(q, nodeData);

the reverse map needs to be updated, too, with something like

Set<V> edgesToQ = reverseAdjacencies.get(q);
if (edgesToQ == null) {
  edgesToQ = new HashSet<>();
  reverseAdjacencies.put(q, edgesToQ);
}
edgesToQ.add(p);

Now to delete node r ,

// Remove the in-edges to r.
for (V p : reverseAdjacencies.remove(r)) {
  adjacencies.get(p).remove(r);
}
// Remove r and all its out-edges
adjacencies.remove(r);

I've left out details like null checks.