We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topological structures of the underlying networks and can be used as visualization tools. We study the stability of community trees and derive a quantity called the total star number (TSN) that presents an upper bound on the change of community trees. Our findings provide a topological interpretation for the stability of communities generated by the CPM.
Cite
@article{arxiv.1710.03924,
title = {A Note on Community Trees in Networks},
author = {Ruqian Chen and Yen-Chi Chen and Wei Guo and Ashis G. Banerjee},
journal= {arXiv preprint arXiv:1710.03924},
year = {2017}
}