Abstract
Recent years have seen tremendous advances in the scientific study of networks, as more and larger data sets of relationships among nodes have become available in many different fields. This has led to pathbreaking discoveries of near-universal network behavior over time, including the principle of preferential attachment and the emergence of scaling in complex networks. Missing from the set of network analysis methods to date is a measure that describes for each node how its relationship (or links) with other nodes changes from one period to the next. Conventional measures of network change for the most part show how the degrees of a node change; these are scalar comparisons. Our contribution is to use, for the first time, the cosine similarity to capture not just the change in degrees of a node but its relationship to other nodes. These are vector (or matrix)-based comparisons, rather than scalar, and we refer to them as “rewiring” coefficients. We apply this measure to three different networks over time to show the differences in the two types of measures. In general, bigger increases in our rewiring measure are associated with larger increases in network density, but this is not always the case.
Highlights
Interest in network analyses has exploded in recent years across diverse disciplines, ranging from the physical [1] to the bioecological [2, 3] and social sciences [4]
To understand and describe a network’s change it is critical to systematically and consistently measure the degree to which interactions among the nodes making up the network change over time
In the Input-Output Table it would be of interest to assess whether the extent of economic rewiring within individual nations affected their response to the Global Financial Crisis (GFC), and ability to rebound
Summary
Citation: Han Y, Goetz SJ (2019) Measuring network rewiring over time. PLoS ONE 14(7): e0220295. https://doi.org/10.1371/journal. pone.0220295 Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was supported in part by the United States Department of Agriculture, National Institute of Food and Agriculture (NIFA) under project #2017-51150-27125 and by the Pennsylvania State University and NIFA Multistate/ Regional Research Appropriations under project #NE1749. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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