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Register a new userSupracentrality Analysis of Temporal Networks with Directed Interlayer Coupling
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Added by
Dane Taylor
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a emph{supracentrality matrix} $mathbb{C}(omega)$, where $omega$ controls the extent to which centrality trajectories change over time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of $mathbb{C}(omega)$ represent emph{joint centralities}, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute emph{marginal} and emph{conditional centralities}. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large $omega$.
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Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes eigenvector-based centralities, including PageRank and hub/authority scores, to provide a common framework for two popular classes of multilayer networks: multiplex networks (which have layers that encode different types of relationships) and temporal networks (in which the relationships change over time). Our approach involves the study of joint, marginal, and conditional supracentralities that one can calculate from the dominant eigenvector of a supracentrality matrix [Taylor et al., 2017], which couples centrality matrices that are associated with individual network layers. We extend this prior work (which was restricted to temporal networks with layers that are coupled by adjacent-in-time coupling) by allowing the layers to be coupled through a (possibly asymmetric) interlayer-adjacency matrix $tilde{{bf A}}$, where the entry $tilde{A}_{tt} geq 0$ encodes the coupling between layers $t$ and $t$. Our framework provides a unifying foundation for centrality analysis of multiplex and temporal networks; it also illustrates a complicated dependency of the supracentralities on the topology and weights of interlayer coupling. By scaling $tilde{{bf A}}$ by an interlayer-coupling strength $omegage0$ and developing a singular perturbation theory for the limits of weak ($omegato0^+$) and strong coupling ($omegatoinfty$), we also reveal an interesting dependence of supracentralities on the dominant left and right eigenvectors of $tilde{{bf A}}$.
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