Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling

  • Dane TaylorEmail author
  • Mason A. Porter
  • Peter J. Mucha
Part of the Computational Social Sciences book series (CSS)


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 supracentrality matrix \(\mathbb {C}(\omega )\), where ω 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 joint centralities, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute marginal and 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 ω.


Temporal networks Centrality PageRank Multilayer networks Multiplex networks 



We thank Petter Holme and Jari Saramäki for the invitation to write this chapter. We thank Deryl DeFord, Tina Eliassi-Rad, Des Higham, Christine Klymko, Marianne McKenzie, Scott Pauls, and Michael Schaub for fruitful conversations. DT was supported by the Simons Foundation under Award #578333. PJM was supported by the James S. McDonnell Foundation 21st Century Science Initiative—Complex Systems Scholar Award #220020315.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Dane Taylor
    • 1
    Email author
  • Mason A. Porter
    • 2
  • Peter J. Mucha
    • 3
  1. 1.University at Buffalo, State University of New YorkBuffaloUSA
  2. 2.University of CaliforniaLos AngelesUSA
  3. 3.University of North CarolinaChapel HillUSA

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