Understand
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 $t'$.