Exact and approximate role assignment for multi-layer networks

The concept of role equivalence has been applied in social network analysis for decades. Early definitions recognized two social actors as role equivalent, if they have identical relationships to the same other actors. Although this rather strong equivalence requirement has been relaxed in different ways, it is often challenging to detect interesting, non-trivial role equivalences, especially for social networks derived from empirical data. Multi-layer networks (MLNs) are increasingly gaining popularity for modelling collective adaptive systems, for example, engineered cyber-physical systems or animal collectives. Multiplex networks, a special case of MLNs, transparently and compactly describe such complex interactions (social, biological, transportation), where nodes can be connected by links of different types. In this work, we first propose a novel notion of exact and approximate role equivalence for multiplex MLNs. Then, we implement and experimentally evaluate the algorithm on a suite of real-world case studies. Results demonstrate that our notion of approximate role assignment not only obtains non-trivial partitions over nodes and layers as well, but it provides a fine-grained hierarchy of role equivalences, which is impossible to obtain by (combining) the existing role detection techniques. We demonstrate the latter by interpreting in detail the case study of Florence families, a classical benchmark from literature.