The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks

TL;DR

This paper reformulates the map equation for community detection as a differentiable neural network-compatible objective, enabling end-to-end learning with node features and automatic cluster number selection, improving performance on graph clustering tasks.

Contribution

It introduces a neural network-compatible, differentiable formulation of the map equation for community detection, allowing end-to-end training and automatic determination of cluster count.

Findings

Achieves competitive results on synthetic and real-world datasets.

Enables integration of node features into community detection.

Supports automatic selection of the number of clusters.

Abstract

Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions, optimised with custom-tailored search algorithms, but often without leveraging recent advances in deep learning. Recently, first works have started incorporating such objectives into loss functions for deep graph clustering and pooling. We consider the map equation, a popular information-theoretic objective function for unsupervised community detection, and express it in differentiable tensor form for optimisation through gradient descent. Our formulation turns the map equation compatible with any neural network architecture, enables end-to-end learning, incorporates node features, and chooses the optimal number of clusters automatically, all without requiring explicit regularisation. Applied to unsupervised graph clustering tasks, we achieve competitive performance against state-of-the-art deep graph clustering baselines in synthetic and real-world datasets.