An adaptation of InfoMap to absorbing random walks using absorption-scaled graphs

TL;DR

This paper adapts the InfoMap community detection algorithm to account for absorbing random walks, modeling heterogeneous node absorption rates, with implications for disease spread dynamics and community structure detection.

Contribution

The authors introduce an absorption-scaled graph adaptation of InfoMap that converges to the standard version as absorption rates approach zero, capturing effects of node heterogeneity.

Findings

Community detection can differ significantly when accounting for absorption rates.

Heterogeneous absorption influences SIR epidemic dynamics on networks.

Moderate absorption rates can maximize outbreak duration in ring-lattice networks.

Abstract

InfoMap is a popular approach to detect densely connected "communities" of nodes in networks. To detect such communities, InfoMap uses random walks and ideas from information theory. Motivated by the dynamics of disease spread on networks, whose nodes can have heterogeneous disease-removal rates, we adapt InfoMap to absorbing random walks. To do this, we use absorption-scaled graphs (in which edge weights are scaled according to absorption rates) and Markov time sweeping. One of our adaptations of InfoMap converges to the standard version of InfoMap in the limit in which the node-absorption rates approach $0$. We demonstrate that the community structure that one obtains using our adaptations of InfoMap can differ markedly from the community structure that one detects using methods that do not account for node-absorption rates. We also illustrate that the community structure that is induced by heterogeneous absorption rates can have important implications for susceptible-infected-recovered (SIR) dynamics on ring-lattice networks. For example, in some situations, the outbreak duration is maximized when a moderate number of nodes have large node-absorption rates.