Calvin Coolidge and the Supreme Court

Fowler, R. M.

doi:10.1111/1059-4329.00012

Cited by 1 publication

(2 citation statements)

References 16 publications

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“…One can also try to reveal insights into large-scale social processes during a given time period (e.g., the identification of which social issues are considered to be important and/or controversial). We study the data set that was made available by Fowler et al [40,41], and we note that the complete decisions are available online from the U.S. government [64]. We examine temporal citation networks for the time range 1800-2002, which we bin into decades to give T = 20 time layers.…”

Section: Citations Of United States Supreme Court Decisions (Scd)mentioning

confidence: 99%

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Eigenvector-Based Centrality Measures for Temporal Networks

Taylor¹,

Myers²,

Clauset³

et al. 2017

Multiscale Model. Simul.

173

198

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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 supra-centrality 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 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.

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Section: Citations Of United States Supreme Court Decisions (Scd)mentioning

confidence: 99%

“…5, we illustrate our approach using three examples from empirical data: Ph.D. exchange using data from the Mathematics Genealogy Project [101] (see Fig. 1.1), top billing in the Golden Age of Hollywood using the Internet Movie Database (IMDb) [63], and citations of United States Supreme Court decisions [40,64]. We conclude in Sec.…”

mentioning

confidence: 99%