JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1081 10.6339/22-JDS1081 Statistical Data Science Flowthrough Centrality: A Stable Node Centrality Measure https://orcid.org/0000-0002-4387-7297 MannCharles F.1 https://orcid.org/0000-0001-9150-7832 McGeeMonnie2 https://orcid.org/0000-0001-7856-1826 OlinickEli V.olinick@smu.edu3∗ MatulaDavid W.4 College of Business, Dallas Baptist University, Dallas, TX, USA Department of Statistical Science, Southern Methodist University, Dallas, TX, USA Department of Operations Research and Engineering Management, Southern Methodist University, Dallas, TX, USA Department of Computer Science, Southern Methodist University, Dallas, TX, USA Corresponding author. Email: olinick@smu.edu. 202322122022214696714 Supplementary Material

Code: The code for this research consists of approximately 160 R Markdown files. The files include R code for the results and graphics as well as data files resulting from the linear programming algorithm in (4), (5), and (6).

30320226122022 2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2023 Open access article under the CC BY license.

This paper introduces flowthrough centrality, a node centrality measure determined from the hierarchical maximum concurrent flow problem (HMCFP). Based upon the extent to which a node is acting as a hub within a network, this centrality measure is defined to be the fraction of the flow passing through the node to the total flow capacity of the node. Flowthrough centrality is compared to the commonly-used centralities of closeness centrality, betweenness centrality, and flow betweenness centrality, as well as to stable betweenness centrality to measure the stability (i.e., accuracy) of the centralities when knowledge of the network topology is incomplete or in transition. Perturbations do not alter the flowthrough centrality values of nodes that are based upon flow as much as they do other types of centrality values that are based upon geodesics. The flowthrough centrality measure overcomes the problem of overstating or understating the roles that significant actors play in social networks. The flowthrough centrality is canonical in that it is determined from a natural, realized flow universally applicable to all networks.

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