In this paper, the authors compute the persistent homology (and barcode) of a random (Erdos-Renyi) network.
For their filtration, they start with the clique complex of the graph, which is the simplicial complex with an n-simplex for each (n+1)-clique present in the graph, and consider the ith skeleton of this for the ith step in the filtration.
I can not work out how you would programme this filtration as a Vietoris-Rips complex, for example. If we embed a graph in a metric space, and say that nodes are distance 1 apart if they are connected in the graph, and some higher distance apart otherwise, then a Vietoris-Rips complex would immediately give you the full clique complex, and I am unsure whether you can make it give you the i skeletons in turn.
I thought about trying to programme it as a Cech complex, but I do not believe Javaplex, which seems to be the most common software in this area, can do Cech complexes.