Eigenvector-based centrality measures for temporal networks

Dane Taylor, Sean A. Myers, Aaron Clauset, Mason A. Porter, Peter J. Mucha

Research output: Research - peer-reviewArticle

  • 6 Citations

Abstract

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvectorbased centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supracentrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of the nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.

LanguageEnglish (US)
Pages537-574
Number of pages38
JournalMultiscale Modeling and Simulation
Volume15
Issue number1
DOIs
StatePublished - 2017

Fingerprint

Centrality
Eigenvector
eigenvectors
Eigenvalues and eigenfunctions
Vertex of a graph
matrix
matrices
Trajectories
Availability
First-order
Term
mathematics
trajectory
perturbation
timescale
decision
method
court
availability
trajectories

Keywords

  • Eigenvector centrality
  • Hubs and authorities
  • Multilayer networks
  • Ranking systems
  • Singular perturbation
  • Temporal networks

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

Taylor, D., Myers, S. A., Clauset, A., Porter, M. A., & Mucha, P. J. (2017). Eigenvector-based centrality measures for temporal networks. Multiscale Modeling and Simulation, 15(1), 537-574. DOI: 10.1137/16M1066142

Eigenvector-based centrality measures for temporal networks. / Taylor, Dane; Myers, Sean A.; Clauset, Aaron; Porter, Mason A.; Mucha, Peter J.

In: Multiscale Modeling and Simulation, Vol. 15, No. 1, 2017, p. 537-574.

Research output: Research - peer-reviewArticle

Taylor, D, Myers, SA, Clauset, A, Porter, MA & Mucha, PJ 2017, 'Eigenvector-based centrality measures for temporal networks' Multiscale Modeling and Simulation, vol 15, no. 1, pp. 537-574. DOI: 10.1137/16M1066142
Taylor D, Myers SA, Clauset A, Porter MA, Mucha PJ. Eigenvector-based centrality measures for temporal networks. Multiscale Modeling and Simulation. 2017;15(1):537-574. Available from, DOI: 10.1137/16M1066142
Taylor, Dane ; Myers, Sean A. ; Clauset, Aaron ; Porter, Mason A. ; Mucha, Peter J./ Eigenvector-based centrality measures for temporal networks. In: Multiscale Modeling and Simulation. 2017 ; Vol. 15, No. 1. pp. 537-574
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