Estimating random walk centrality in networks

Brad C. Johnson and Steve Kirkland

Computational Statistics & Data Analysis, 2019, vol. 138, issue C, 190-200

Abstract: Random walk centrality (equivalently, the accessibility index) for the states of a time-homogeneous irreducible Markov chain on a finite state space is considered. It is known that the accessibility index for a particular state can be written in terms of the first and second moments of the first return time to that state. Based on that observation, the problem of estimating the random walk centrality of a state is approached by taking realizations of the Markov chain, and then statistically estimating the first two moments of the corresponding first return time. In addition to the estimate of the random walk centrality, this method also yields the standard error, the bias and a confidence interval for that estimate. For the case that the directed graph of the transition matrix for the Markov chain has a cut-point, an alternate strategy for computing the random walk centrality is outlined that may be of use when the centrality values are of interest for only some of the states. In order to illustrate the effectiveness of the results, estimates of the random walk centrality arising from random walks for several directed and undirected graphs are discussed.

Keywords: Random walk centrality; Network centrality; Accessibility index; Markov chains; Mean first passage times; Bootstrap (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947319300933
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:138:y:2019:i:c:p:190-200

DOI: 10.1016/j.csda.2019.04.009

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().