The Concentration and Stability of the Community Detecting Functions on Random Networks

TL;DR

This paper introduces a general framework for community detection functions in random networks, analyzing their concentration and stability properties using probabilistic methods, with applications to various network models.

Contribution

It proposes a unified form of community detection functions and derives concentration inequalities for their values on different types of random networks.

Findings

Derived LDP inequalities for community detection functions.

Analyzed concentration and stability on sparse and non-sparse networks.

Applied results to ER and CL network models.

Abstract

We propose a general form of community detecting functions for finding the communities or the optimal partition of a random network, and examine the concentration and stability of the function values using the bounded difference martingale method. We derive LDP inequalities for both the general case and several specific community detecting functions: modularity, graph bipartitioning and q-Potts community structure. We also discuss the concentration and stability of community detecting functions on different types of random networks: the sparse and non-sparse networks and some examples such as ER and CL networks.