Inference of Hierarchical Core-Periphery Structure in Temporal Networks

TL;DR

This paper introduces a novel method for detecting hierarchical core-periphery structures in temporal networks using multilayer network representations and stochastic block models, extending previous approaches to dynamic settings.

Contribution

It generalizes existing core-periphery detection methods to temporal networks and accommodates various hierarchical and non-nested mesoscale structures.

Findings

Successfully applied to real-world temporal networks

Identified diverse core-periphery structures in dynamic data

Enhanced understanding of mesoscale structures over time

Abstract

Networks can have various types of mesoscale structures. One type of mesoscale structure in networks is core-periphery structure, which consists of densely-connected core nodes and sparsely-connected peripheral nodes. The core nodes are connected densely to each other and can be connected to the peripheral nodes, which are connected sparsely to other nodes. There has been much research on core-periphery structure in time-independent networks, but few core-periphery detection methods have been developed for time-dependent (i.e., ``temporal") networks. Using a multilayer-network representation of temporal networks and an inference approach that employs stochastic block models, we generalize a recent method for detecting hierarchical core-periphery structure \cite{Polanco23} from time-independent networks to temporal networks. In contrast to ``onion-like'' nested core-periphery structures (where each node is assigned to a group according to how deeply it is nested in a network's core), hierarchical core-periphery structures encompass networks with nested structures, tree-like structures (where any two groups must either be disjoint or have one as a strict subset of the other), and general non-nested mesoscale structures (where the group assignments of nodes do not have to be nested in any way). To perform statistical inference and thereby identify core-periphery structure, we use a Markov-chain Monte Carlo (MCMC) approach. We illustrate our method for detecting hierarchical core-periphery structure in two real-world temporal networks, and we briefly discuss the structures that we identify in these networks.