Year: 2020
Type: article
Abstract: We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different timescales. The specific implementation of the quality function and the resulting optimal community structure thus become dependent both on the type of Markov process and on the specific Markov times considered. For instance, if we use a natural Markov chain dynamics and discount its stationary distribution (that is, we take as reference process the dynamics at infinite time) we obtain the standard formulation of the Markov stability. Notably, the possibility to use finite-time transition probabilities to define the reference process naturally allows detecting communities at different resolutions, without the need to consider a continuous-time Markov chain in the small time limit. The main advantage of our general formulation of Markov stability based on dynamical flows is that we work with lumped Markov chains on network partitions, having the same stationary distribution of the original process. In this way the form of the quality function becomes invariant under partitioning, leading to a self-consistent definition of community structures at different aggregation scales.
Source: Physical review. E
Institutions: Centre National de la Recherche Scientifique, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Université Paris-Saclay, CEA Paris-Saclay - Etablissement de Saclay, Service de Physique de l'État Condensé, CEA Paris-Saclay, Institute for Complex Systems, Sapienza University of Rome, Roma Tre University, University of Rome Tor Vergata
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2938904807