An adaptation of InfoMap to absorbing random walks using absorption-scaled graphs
This work addresses community detection in networks with absorption dynamics, relevant for modeling disease spread, but it is incremental as it adapts an existing method.
The authors tackled the problem of detecting communities in networks with heterogeneous node-absorption rates, adapting InfoMap to absorbing random walks using absorption-scaled graphs and Markov time sweeping, resulting in community structures that differ from standard methods and impact SIR dynamics, such as maximizing outbreak duration with moderate absorption rates.
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.