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.

网络相似性度量量化了两个网络如何以及何时对称相关，包括统计关联的度量，例如成对距离或网络之间或多重网络层之间的其他相关度量，但都不能直接揭示是否存在隐藏的混杂网络因素或他们能否估计这种相关性何时以因果关系为基础。在这项工作中，我们将这个成对概念框架扩展到网络的三元组，并量化网络如何以及何时直接或通过间接中介或与第三个网络的交互与第二个网络（具有相同数量的节点）相关。因此，我们开发了一种简单直观的集合论方法来量化网络之间的中介和抑制。