Question

I am implementing an algorithm for finding a dense subgraph in a directed graph using python+igraph. The main loop maintains two subgraphs S and T which are initially identical and removes nodes (and incident edges) accoriding to a count of the indegree (or outdegree) of those nodes with respect to the other graph. The problem I have is that igraph renumbers the vertices so when I delete some from T, the remaining nodes no longer correspond to the same ones in S.

Here is the main part of the loop that is key.

def directed(S):
    T = S.copy()
    c = 2
    while(S.vcount() > 0 and T.vcount() > 0):
        if (S.vcount()/T.vcount() > c):
            AS = S.vs.select(lambda vertex: T.outdegree(vertex) < 1.01*E(S,T)/S.vcount())
            S.delete_vertices(AS)
        else:
            BT = T.vs.select(lambda vertex: S.indegree(vertex) < 1.01*E(S,T)/T.vcount())
            T.delete_vertices(BT)

This doesn’t work because of the effect of deleting vertices on the vertex ids. Is there a standard workaround for this problem?

Answer 1

One possibility is to assign unique names to the vertices in the name vertex attribute. These are kept intact when vertices are removed (unlike vertex IDs), and you can use them to refer to vertices in functions like indegree or outdegree. E.g.:

>>> g = Graph.Ring(4)
>>> g.vs["name"] = ["A", "B", "C", "D"]
>>> g.degree("C")
2
>>> g.delete_vertices(["B"])
>>> g.degree("C")
1

Note that I have removed vertex B so vertex C also gained a new ID, but the name is still the same.

In your case, the row with the select condition could probably be re-written like this:

AS = S.vs.select(lambda vertex: T.outdegree(vertex["name"]) < 1.01 * E(S,T)/S.vcount())

Of course this assumes that initially the vertex names are the same in S and T.