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Abstract
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.
Highlights
As a final analysis, and in order to show how suppression and mediation can be functionally modulated within a particular realworld example, we examine the role played by the proximity layer in the relation between the Facebook and phone calls/SMS layers when such layer is systematically varied
In this paper, we have proposed a simple strategy to assess the role that a given network might play in shaping the relation between two other networks, enlarging the paradigm of network similarity beyond the classical pairwise comparison
We explore the coexistence between mediation and suppression and develop a procedure to disentangle both indirect effects
Summary
It is worth to stress that for large networks the finite-size effects become less common, and ΔR,{S,M} will tend to zero, for all the realisations, resulting in a small standard deviation, and in any value of suppression and mediation being highly significant. The original value of Δ is very close to zero, as well as the ones obtained from full randomisation of B Since in this example the networks are independent, any mediation or suppression is only a spurious residual due to finite-size effects, this residual is flagged out in similar terms by a selective rewiring on the actual network B (ΔX) or on its full randomisation (ΔRX), the violet and green histograms overlap, and the pink and pale blue ones overlap.
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