InfoMap for absorbing random walks

Community structure is a network feature in which densely connected sets of nodes (that are called communities) are sparsely connected to other densely connected set of nodes. This feature can significantly impact dynamics on the network. For example, community structure can affect attributes of disease dynamics such as outbreak size, outbreak duration, and outbreak peak. In turn, attributes of dynamics can affect community structure. For example, the recovery rates of a disease can be a barrier for the transmission of the disease within a community. In this context, we can interpret the recovery rates as "absorption" of a random walker representing the transmission of the disease. We give an algorithm that outputs communities that are informed by both the edges of the network and node absorption. To this end, we adapt the random-walk based algorithm InfoMap. Intuitively, InfoMap produces communities such that one step of a random walker of a non-absorbing random walk is more likely to occur within a community than between two distinct communities. We use absorption-scaled graphs and Markov time sweeping to adapt InfoMap to absorbing random walks. We apply our algorithm to study the effect on susceptible-infected-recovered dynamics of communities informed by absorption.