Algorithmic infeasibility of community detection in higher-order networks

TL;DR

This paper analyzes the limits of community detection in complex higher-order networks, revealing that increased network complexity can hinder algorithmic detectability and sometimes lower-order networks perform better.

Contribution

It derives the detectability threshold for EM with BP in higher-order networks, highlighting the algorithmic infeasibility of extracting rich information.

Findings

Existence of a phase where lower-order networks outperform higher-order ones in community detection

Analytical derivation of the detectability threshold for EM with BP in higher-order networks

Higher complexity can lead to algorithmic infeasibility in community detection

Abstract

In principle, higher-order networks that have multiple edge types are more informative than their lower-order counterparts. In practice, however, excessively rich information may be algorithmically infeasible to extract. It requires an algorithm that assumes a high-dimensional model and such an algorithm may perform poorly or be extremely sensitive to the initial estimate of the model parameters. Herein, we address this problem of community detection through a detectability analysis. We focus on the expectation-maximization (EM) algorithm with belief propagation (BP), and analytically derive its algorithmic detectability threshold, i.e., the limit of the modular structure strength below which the algorithm can no longer detect any modular structures. The results indicate the existence of a phase in which the community detection of a lower-order network outperforms its higher-order counterpart.