Resistance-distance betweenness: Definition, properties, and application in complex linguistic networks

Abstract

Betweenness centrality measures how a node lies on the paths between other nodes. We propose the so-called resistance-distance betweenness (RDB) which takes a new viewpoint on scoring paths and contribution of each node in the paths. This new betweenness is developed based on the two facts: (1) the resistance distance characterizes the aggregate distance between two nodes in the context of electrical networks; (2) the resistance distance has an edge-wise decomposition form. Thus, the RDB of a node is defined as the sum of resistance distance components associated with the node’s incident edges, which measures how a node lies on the “aggregated path” between other nodes. The basic properties of RDB and its relation and difference from current-flow betweenness (CFB) are investigated. Then, we apply the RDB to the study of an open question in linguistic networks, i.e., to check whether the Yuan poems written by Han and non-Han poets are similar. We also compare the performance of RDB with CFB. The betweenness analysis of the character co-occurrence networks of Han’s and non-Han’s poems provides a fresh and quantitative perspective to support that Han’s and non-Han’s poems are similar in general.