Phase transition in the detection of modules in sparse networks

TL;DR

This paper analyzes the phase transition in detecting communities in sparse networks, revealing a critical point where detection shifts from impossible to possible, and distinguishes between computationally hard and easy regions.

Contribution

It provides an asymptotically exact analysis of community detection phase transitions in sparse networks using the cavity method, and offers a practical detection algorithm.

Findings

Identifies a phase transition in detectability of communities.

Distinguishes between algorithmically hard and easy detection regions.

Provides a practical algorithm for module detection and parameter learning.

Abstract

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks. Our results are also applicable to detection of functional modules, partitions, and colorings in noisy planted models. Using a cavity method analysis, we unveil a phase transition from a region where the original group assignment is undetectable to one where detection is possible. In some cases, the detectable region splits into an algorithmically hard region and an easy one. Our approach naturally translates into a practical algorithm for detecting modules in sparse networks, and learning the parameters of the underlying model.