Temporal_Eigenvector_Centrality. This Matlab code includes scripts and a demo for computing eigenvector centralities for temporal networks. Eigenvector-based centrality measures for temporal networks. 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 eigenvector-based 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.
Keywords for this software
References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Taylor, Dane; Porter, Mason A.; Mucha, Peter J.: Tunable eigenvector-based centralities for multiplex and temporal networks (2021)
- Zhang, Ting; Zhang, Kun; Lv, Laishui; Bardou, Dalal: Co-ranking for nodes, layers and timestamps in multilayer temporal networks (2019)
- Flores, Julio; Romance, Miguel: On eigenvector-like centralities for temporal networks: discrete vs. continuous time scales (2018)
- Fenu, Caterina; Higham, Desmond J.: Block matrix formulations for evolving networks (2017)
- Liao, Hao; Mariani, Manuel Sebastian; Medo, Matúš; Zhang, Yi-Cheng; Zhou, Ming-Yang: Ranking in evolving complex networks (2017)
- Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud: Random walks and diffusion on networks (2017)
- Taylor, Dane; Myers, Sean A.; Clauset, Aaron; Porter, Mason A.; Mucha, Peter J.: Eigenvector-based centrality measures for temporal networks (2017)
- Taylor, Dane; Skardal, Per Sebastian; Sun, Jie: Synchronization of heterogeneous oscillators under network modifications: perturbation and optimization of the synchrony alignment function (2016)