This is APAL by Osman Doluca and Kaya Oğuz, implemented back in 2018-2019.

Please cite: Doluca, O., & Oğuz, K. (2021). APAL: Adjacency Propagation Algorithm for overlapping community detection in biological networks. Information Sciences, 579, 574-590. https://www.sciencedirect.com/science/article/abs/pii/S0020025521008318

APAL has been extended to work on weighted networks. See WAPAL for more information: https://github.com/koguz/WAPAL/

APAL uses its own implementation of the Graph ADT. It is very straightforward to use this Graph class.

from Graph import *

g = Graph()
# add a vertex, the type can be anything, int, string or any other class
g.add_vertex(1) 
# or a list of vertices
g.add_vertices([1, 2, 3, 4])
# then, add an edge, say between 1 and 3
g.add_edge(1, 3)
# or a list of edges to a vertex
g.add_edges(2, [3, 4])

Once a graph is populated with vertices and edges, you can use it in APAL.

To run APAL, create an APAL object, assign your graph to it. Then, run run_apal(t) with the threshold value t, between 0 and 1.

from APAL import *

apal = APAL()
apal.graph = g # the graph we have defined above
apal_clusters = apal.run_apal(0.75)

The overlapping communities found in Graph g will be in the apal_clusters variable. This repository also includes the CompareClusters class so that you can compare the result to a ground truth, if you have one. Assuming that the real clusters are in clusters variable, use it as follows for normalised mutual information (NMI) metric that is extended for overlapping communities as detailed in

Andrea Lancichinetti et al 2009 New J. Phys. 11 033015, https://iopscience.iop.org/article/10.1088/1367-2630/11/3/033015

The result has a range of [0,1] where values closer to 1 are of communities that are more alike, therefore represent better results.

from CompareClusters import CompareClusters as CC

cc = CC(g.vertices, clusters, apal_clusters)
apal_result = cc.nvi_overlapping()

This is an implementation of OGG discussed in the APAL paper. Simply create an OGG object and provide the parameters to generate a random graph that contains communities that overlap.

from OGG import *

ogg = OGG()
ogg.number_of_clusters = 10
ogg.average_cluster_size = 15
ogg.overlapping = 0.3
ogg.interconnectivity = 0.6
ogg.intraconnectivity = 0.6
ogg.generate_graph()

Once ogg.generate_graph() runs, the graph can be accessed with the variable ogg.graph and the clusters by the variable ogg.clusters.