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Article overview
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Eigenvector-Based Centrality Measures for Temporal Networks | | Dane Taylor
; Sean A. Myers
; Aaron Clauset
; Mason A. Porter
; Peter J. Mucha
; | | Date: |
5 Jul 2015 | | Abstract: | In the study of static networks, numerous "centrality" measures have been
developed to quantify the importances of nodes in networks, and one can express
many of these measures in terms of the leading eigenvector of a matrix. With
the increasing availability of network data that changes in time, it is
important to extend eigenvector-based centrality measures to time-dependent
networks. In this paper, we introduce a principled generalization that is valid
for any eigenvector-based centrality measure in terms of matrices of size
$NT imes NT$, where the components of the dominant eigenvector of such a
matrix describes the centralities of $N$ nodes during $T$ time layers. Our
approach relies on coupling centrality values between neighboring time layers
with a inter-layer edge, whose weight controls the extent to which centrality
trajectories change over time. By studying the limit of strong coupling between
layers, 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 nodes’ centrality changes over time. Importantly, we
compute these quantities by solving linear algebraic equations of dimension
$N$. This is much more computationally efficient than computing the dominant
eigenvector of the full $NT imes NT$ matrix. 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 Supreme Court of the
United States. | | Source: | arXiv, 1507.1266 | | Services: | Forum | Review | PDF | Favorites | |
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