Distributed Community Detection in Dynamic Graphs

TL;DR

This paper introduces a distributed community detection protocol for dynamic graphs modeled by a stochastic process, achieving accurate detection in logarithmic time even with sparse, disconnected snapshots, advancing understanding of self-organizing social networks.

Contribution

It proposes a novel distributed protocol based on label propagation for dynamic graphs and proves its effectiveness under certain probabilistic conditions.

Findings

Protocol finds the correct community partition in O(log n) time.

Effective even with sparse, disconnected graph snapshots.

Works when the community edge probability ratio exceeds a small polynomial in n.

Abstract

Inspired by the increasing interest in self-organizing social opportunistic networks, we investigate the problem of distributed detection of unknown communities in dynamic random graphs. As a formal framework, we consider the dynamic version of the well-studied \emph{Planted Bisection Model} $\sdG(n,p,q)$ where the node set $[n]$ of the network is partitioned into two unknown communities and, at every time step, each possible edge $(u,v)$ is active with probability $p$ if both nodes belong to the same community, while it is active with probability $q$ (with $q<<p$) otherwise. We also consider a time-Markovian generalization of this model. We propose a distributed protocol based on the popular \emph{Label Propagation Algorithm} and prove that, when the ratio $p/q$ is larger than $n^{b}$ (for an arbitrarily small constant $b>0$), the protocol finds the right "planted" partition in $O(\log n)$ time even when the snapshots of the dynamic graph are sparse and disconnected (i.e. in the case $p=\Theta(1/n)$).