  Multiplex networks, a special type of multilayer networks, are increasingly
applied in many domains ranging from social media analytics to biology. A
common task in these applications concerns the detection of community
structures. Many existing algorithms for community detection in multiplexes
attempt to detect communities which are shared by all layers. In this article
we propose a community detection algorithm, LART (Locally Adaptive Random
Transitions), for the detection of communities that are shared by either some
or all the layers in the multiplex. The algorithm is based on a random walk on
the multiplex, and the transition probabilities defining the random walk are
allowed to depend on the local topological similarity between layers at any
given node so as to facilitate the exploration of communities across layers.
Based on this random walk, a node dissimilarity measure is derived and nodes
are clustered based on this distance in a hierarchical fashion. We present
experimental results using networks simulated under various scenarios to
showcase the performance of LART in comparison to related community detection
algorithms.
