A measure of centrality based on a reciprocally perturbed Markov chainfor asymmetric relations. Issue 3 (3rd July 2022)

• Record Type: Journal Article
• Authors: Lu, Neng-Pin
• Is Part Of: Journal of mathematical sociology. Volume 46:Issue 3(2022)
• Page Start: 246
• Page End: 265
• Publication Date: 2022-07-03
• Subjects: Perturbation -- Markov chain -- centrality; Sociology -- Periodicals; Sociology -- Mathematical models -- Periodicals; 301.0151
• DOI: 10.1080/0022250X.2021.1885402
• Languages: English
• ISSNs: 0022-250X

Abstract

ABSTRACT: In digraphs representing asymmetric relations, the measured scores of previous spectral rankings are usually dominated by nodes in the largest strongly connected component. In our previous work, we proposed hierarchical alpha centrality to give higher scores for more reachable nodes not in the largest strongly connected component. However, without careful consideration of damping parameters, the scores obtained by this method may be unbounded. In this paper, we normalize the adjacency matrix to be stochastic, subsequently damping the resulting Markov chain with a reciprocal perturbation at each and every non-zero transition, and propose a new hierarchical measure of centrality for asymmetric relations. The proposed measure simplifies damping and ensures that the measured scores are bounded.