A measure of centrality based on a reciprocally perturbed Markov chainfor asymmetric relations

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.

KEYWORDS:

• Perturbation
• Markov chain
• centrality

Acknowledgments

The author would like to thank the editors and reviewers for their valuable comments and insightful suggestions to improve the paper, which was supported in part by the Ministry of Science and Technology, Taiwan, R.O.C., under Grant MOST 108-2410-H-182-017.

Notes

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Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taiwan, R.O.C. [MOST 108-2410-H-182-017].