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I have a directed graph with continuous values on each edge -- the
number of transferred patients that flow between any pair of
hospitals in the United States. I need a continuous measure of
centrality that increases with the degree of the receiving hospital,
the number of patients transferred between any pair of hospitals, and
also increases in the centrality of the hospitals that themselves
send the patients.
Katz' Rank Prestige, PageRank and Bonacich Power all have these
properties, and all are more-or-less readily implemented. Is there a
simple mathematical relationship between the three? Is there a
compelling reason to choose among them? (And for those who prefer
Bonacich, do you have an a prioiri way to choose the beta?)
I would welcome advice.
The relevant references are:
Bonacich, P. 1987. "Power and Centrality: A Family of Measures."
American Journal of Sociology 92:1170-1182.
Brin, Sergey, and Lawrence Page. 1998. "The Anatomy of a Large-Scale
Hypertextual Web Search Engine." WWW7 / Computer Networks 30:110-117.
Page, Lawrence, Sergey Brin, Rajeev Motwani, and Terry Winograd.
1999. "The PageRank Citation Ranking: Bringing Order to the Web."
Katz, L. 1953. "A New Status Index Derived from Sociometric
Analysis." Psychometrika 18:39-43.
Theodore J. Iwashyna, M.D., Ph.D.
Division of Pulmonary and Critical Care
Department of Medicine
Hospital of the University of Pennsylvania
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