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Abstract
Multiplex networks (a system of multiple networks that have different types of links but share a common set of nodes) arise naturally in a wide spectrum of fields. Theoretical studies show that in such multiplex networks, correlated edge dynamics between the layers can have a profound effect on dynamical processes. However, how to extract the correlations from real-world systems is an outstanding challenge. Here we introduce the Multiplex Markov chain to quantify correlations in edge dynamics found in longitudinal data of multiplex networks. By comparing the results obtained from the multiplex perspective to a null model which assumes layers in a network are independent, we can identify real correlations as distinct from simultaneous changes that occur due to random chance. We use this approach on two different data sets: the network of trade and alliances between nation states, and the email and co-commit networks between developers of open source software. We establish the existence of “dynamical spillover” showing the correlated formation (or deletion) of edges of different types as the system evolves. The details of the dynamics over time provide insight into potential causal pathways.
Highlights
Multiplex networks arise naturally in a wide spectrum of fields
We illustrate the tool by applying it to two different multiplex data sets: a network of trade and alliances between nation states; and the co-commit and email networks of developers of an open source software. We show that these networks exhibit dynamical spillover, i.e., the edge dynamics on a layer of these multiplex networks are strongly influenced by the presence of edges in another layer
We present the Multiplex Markov chain model that quantifies the correlations present in the edge dynamics occurring on two layers of a multiplex network, and the corresponding null model that helps us distinguish non-trivial correlations from those that occur due to randomness
Summary
Multiplex networks (a system of multiple networks that have different types of links but share a common set of nodes) arise naturally in a wide spectrum of fields. By comparing the results obtained from the multiplex perspective to a null model which assumes layers in a network are independent, we can identify real correlations as distinct from simultaneous changes that occur due to random chance We use this approach on two different data sets: the network of trade and alliances between nation states, and the email and co-commit networks between developers of open source software. Multiplex networks are networks that share a common set of nodes that can be linked via different types of edges that comprise the system Examples of such systems include networks of nation states that have many types of relationships such as trade, alliances, military conflicts etc.; communication networks of individuals who might communicate by email, or over a social networking website; and a transportation network of a city which consists of systems such as road and railway connections. The works discussed above explore the presence of correlations in static snapshots, whereas our focus is on correlations in longitudinal evolution
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