  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.
