Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs

• URL: http://arxiv.org/abs/2301.11120v1
• Date: Mon, 16 Jan 2023 12:45:33 GMT
• Title: Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs
• Authors: Luka V. Petrovi\'c, Vincenzo Perri
• Abstract summary: mesoscale structures are integral part of the abstraction and analysis of complex systems. They can represent communities in social or citation networks, roles in corporate interactions, or core-periphery structures in transportation networks. We derive a Bayesian approach that simultaneously models the optimal partitioning of nodes in groups and the optimal higher-order network dynamics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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