An Algorithm for Finding Equitable Clusters in Multi-Layer Networks

This paper is concerned with the analysis of multi-layer networks consisting of different kinds of oscillators and couplings. In particular, we propose an algorithm for finding equitable clusters in this general class of networks, thus generalizing an existing algorithm specific for networks with identical nodes and one kind of connections. The algorithm is suitable to analyze complex networks of particular interest for the scientific community, such as neuron networks and electrical networks. The algorithm is tested on a random heterogeneous network with 40 oscillators of two different kinds and couplings of two different kinds. The stability of the obtained clusters is checked in a two-dimensional parameter space by using brute-force simulations.