Adjustable reach in a network centrality based on current flows
Abstract
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given purpose and network. Here we identify two categories of centrality parameters. Reach parameters control the attenuation of influence flows between distant nodes. Grasp parameters control the centrality's tendency to send influence flows along multiple, often nongeodesic paths. Combining these categories with Borgatti's centrality types [Borgatti, Soc. Networks 27, 55 (2005), 10.1016/j.socnet.2004.11.008], we arrive at a classification system for parametrized centralities. Using this classification, we identify the notable absence of any centrality measures that are radial, reach parametrized, and based on acyclic, conserved flows of influence. We therefore introduce the groundcurrent centrality, which is a measure of precisely this type. Because of its unique position in the taxonomy, the groundcurrent centrality differs significantly from similar centralities. We demonstrate that, compared to other conservedflow centralities, it has a simpler mathematical description. Compared to other reachparametrized centralities, it robustly preserves an intuitive rank ordering across a wide range of network architectures, capturing aspects of both the closeness and betweenness centralities. We also show that it produces a consistent distribution of centrality values among the nodes, neither trivially equally spread (delocalization) nor overly focused on a few nodes (localization). Other reachparametrized centralities exhibit both of these behaviors on regular networks and hub networks, respectively. We compare the properties of the groundcurrent centrality with several other reachparametrized centralities on four artificial networks and seven realworld networks.
 Publication:

Physical Review E
 Pub Date:
 May 2021
 DOI:
 10.1103/PhysRevE.103.052308
 arXiv:
 arXiv:2005.14356
 Bibcode:
 2021PhRvE.103e2308G
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks
 EPrint:
 Phys. Rev. E 103, 052308 (2021)