I have been trying to implement a algorithm but got stuck in finding expectation of the size of the subgraph.
n - size of the network.
d - at most number of communities a node could participate in.
gamma - fraction of ties of nodes in communities .
k - maximum size of a community.
delta - each community size lies between delta*k and k.
epsilon - It is the gap(If for a node 'u' in a community 'C' 'u' has about alpha edges in the community and for the nodes outside the community it has less than alpha-epsilon fraction of connections in the community).
S - sub graph.
Γ(v) - neighborhood of node v in graph G.
And my main issue is with the second point which says size of the sample is less than 3 times expected(need some help with how to calculate and its relationship with the equation give below that).
The following link has the snapshot of the points.snapshot of Algorithm
Link to the research paper http://web.eecs.umich.edu/~schoeneb/papers/OverlappingCompostsoc.pdf