A principal component analysis of 39 scientific impact measures

The impact of scientific publications has traditionally been expressed in terms of citation counts. However, scientific activity has moved online over the past decade. To better capture scientific impact in the digital era, a variety of new impact measures has been proposed on the basis of social network analysis and usage log data. Here we investigate how these new measures relate to each other, and how accurately and completely they express scientific impact. We performed a principal component analysis of the rankings produced by 39 existing and proposed measures of scholarly impact that were calculated on the basis of both citation and usage log data. Our results indicate that the notion of scientific impact is a multi-dimensional construct that can not be adequately measured by any single indicator, although some measures are more suitable than others. The commonly used citation Impact Factor is not positioned at the core of this construct, but at its periphery, and should thus be used with caution

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 supra-centrality matrix of size NTxNT 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.Comment: 38 pages, 7 figures, and 5 table