Phase Transitions in Spectral Community Detection of Large Noisy Networks

TL;DR

This paper analyzes the phase transition phenomena in spectral community detection within large noisy networks, identifying critical thresholds where detection performance sharply declines, and proposes methods to estimate these thresholds from data.

Contribution

It provides theoretical bounds for the detectability phase transition in spectral clustering under noisy conditions, validated by simulations, and introduces a data-driven threshold estimation method.

Findings

Identifies critical edge connection probabilities for community detectability.

Derives bounds on phase transition thresholds that are tight for equal-sized communities.

Validates theoretical results with network simulations.

Abstract

In this paper, we study the sensitivity of the spectral clustering based community detection algorithm subject to a Erdos-Renyi type random noise model. We prove phase transitions in community detectability as a function of the external edge connection probability and the noisy edge presence probability under a general network model where two arbitrarily connected communities are interconnected by random external edges. Specifically, the community detection performance transitions from almost perfect detectability to low detectability as the inter-community edge connection probability exceeds some critical value. We derive upper and lower bounds on the critical value and show that the bounds are identical when the two communities have the same size. The phase transition results are validated using network simulations. Using the derived expressions for the phase transition threshold we propose a method for estimating this threshold from observed data.