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

InfoMap is a popular approach for detecting 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 may have heterogeneous disease-removal rates, we adapt InfoMap to absorbing random walks. To do this, we use absorption-scaled graphs, in which the edge weights are scaled according to absorption rates, along with 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 $0$. The community structure that we obtain using our adaptations of InfoMap can differ markedly from the community structure that one detects using methods that do not take node-absorption rates into account. Additionally, we demonstrate that the community structure that is induced by local dynamics can have important implications for susceptible-infected-recovered (SIR) dynamics on ring-lattice networks. For example, we find situations in which the outbreak duration is maximized when a moderate number of nodes have large node-absorption rates.