Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs

TL;DR

This paper introduces a Bayesian method for detecting mesoscale structures in pathway data on graphs, accounting for dependencies in interactions using higher-order network models, which improves interpretability and detection accuracy.

Contribution

It presents a novel Bayesian approach that models both node partitioning and higher-order network dynamics, addressing limitations of independence assumptions in mesoscale structure detection.

Findings

Successfully recovers community and role-based groupings in synthetic data

Performs competitively on real-world data compared to baseline methods

Provides interpretable insights into network dynamics

Abstract

Mesoscale structures are an integral part of the abstraction and analysis of complex systems. They reveal a node's function in the network, and facilitate our understanding of the network dynamics. For example, they can represent communities in social or citation networks, roles in corporate interactions, or core-periphery structures in transportation networks. We usually detect mesoscale structures under the assumption of independence of interactions. Still, in many cases, the interactions invalidate this assumption by occurring in a specific order. Such patterns emerge in pathway data; to capture them, we have to model the dependencies between interactions using higher-order network models. However, the detection of mesoscale structures in higher-order networks is still under-researched. In this work, we derive a Bayesian approach that simultaneously models the optimal partitioning of nodes in groups and the optimal higher-order network dynamics between the groups. In synthetic data we demonstrate that our method can recover both standard proximity-based communities and role-based groupings of nodes. In synthetic and real world data we show that it can compete with baseline techniques, while additionally providing interpretable abstractions of network dynamics.