Beyond pairwise network similarity: exploring mediation and suppression between networks

Network similarity measures quantify how and when two networks are symmetrically related, including measures of statistical association such as pairwise distance or other correlation measures between networks or between the layers of a multiplex network, but neither can directly unveil whether there are hidden confounding network factors nor can they estimate when such correlation is underpinned by a causal relation. In this work we extend this pairwise conceptual framework to triplets of networks and quantify how and when a network is related to a second network (of the same number of nodes) directly or via the indirect mediation or interaction with a third network. Accordingly, we develop a simple and intuitive set-theoretic approach to quantify mediation and suppression between networks. We validate our theory with synthetic models and further apply it to triplets (multiplex) of real-world networks, unveiling mediation and suppression effects which emerge when considering different modes of interaction in online social networks and different routes of information processing in the nervous system. Mediation analysis aims to clarify the nature of the relationship between two variables, by elucidating the role of a third variable, which can allow or suppress the relationship, or being simply not involved in the process. The authors introduce this framework in the analysis of three-layered multiplex networks, assessing whether a link between two nodes in one layer affects the probability of having a link between the two same nodes in the other two layers, and present some applications to social and biological networks.