Multiplex/Temporal modularity score

[ulgenklc]

Hello Vincent

I have been using leidenalg for years, and I would like to thank you for your work.

My question is if there is a helper function within leidenalg or igraph that calculates the multilayer modularity score for a given quality function and VertexPartition, similar to G.modularity() in igraph?

In particular, for a given list of upper triangular np.arrays of adjacency matrices (list_adjacency):

length = len(list_adjacency)
size = list_adjacency[0].shape[0]
Gs = []
for l in range(length):
  conn_indices = np.where(list_adjacency[l])
  weights = list_adjacency[l][conn_indices] # get the weights corresponding to these indices
  edges = zip(*conn_indices) # a sequence of (i, j) tuples, each corresponding to an edge from i -> j
  G = ig.Graph(n = size, edges=edges, directed=False)# initialize the graph from the edge sequence
  G.vs['id'] = list(range(list_adjacency[l].shape[0]))
  G.vs['node_size'] = 0
  G.es['weight'] = weights #assign node names and weights to be attributes of the vertices and edgesrespectively
  Gs.append(G)

I'm trying to compute the Multilayer Modularity score (or whatever quality function is being used) for the interslice_partition below:

layers, interslice_layer, G_full = time_slices_to_layers(Gs)
partitions = [la.RBConfigurationVertexPartition(H, weights = 'weight', resolution_parameter = 0.98) for H in layers]
interslice_partition = la.RBConfigurationVertexPartition(interslice_layer, weights = 'weight', resolution_parameter = 0)
optimiser = la.Optimiser()
diff = optimiser.optimise_partition_multiplex(partitions + [interslice_partition], n_iterations = 10)

Something like:

G_full.multiplex_modularity(interslice_partition._membership, weights='weight', resolution=0.98, directed=False, VertexPart = la.RBConfigurationVertexPartition)

Note that last argument VertexPart would indicate the quality function that is used, which is different from G.modularity().

Thank you