Measuring the Power of Nodes in Digraphs

21 Pages Posted: 31 Oct 2001

See all articles by P. Jean-Jacques Herings

P. Jean-Jacques Herings

Tilburg University

Gerard van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Dolf Talman

Tilburg University - Department of Econometrics & Operations Research

Date Written: October 5, 2001

Abstract

Many economic and social situations can be represented by a digraph. Both axiomatic and iterative methods to determine the strength or power of all the nodes in a digraph have been proposed in the literature. We propose a new method, where the power of a node is determined by both the number of its successors, as in axiomatic methods, and the powers of its successors, as in iterative methods. Contrary to other iterative methods, we obtain a full ranking of the nodes for any digraph. The new power function, called the positional power function, can either be determined as the unique solution to a system of equations, or as the limit point of an iterative process. The solution is also explicitly characterized. This characterization enables us to derive a number of interesting properties of the positional power function. Next we consider a number of extensions, like the positional weakness function and the position function.

Suggested Citation

Herings, P. Jean-Jacques and van der Laan, Gerard and Talman, Dolf J. J., Measuring the Power of Nodes in Digraphs (October 5, 2001). Available at SSRN: https://ssrn.com/abstract=288088 or http://dx.doi.org/10.2139/ssrn.288088

P. Jean-Jacques Herings (Contact Author)

Tilburg University ( email )

Department of Econometrics and Operations Research
P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4668797 (Phone)
5000 LE (Fax)

HOME PAGE: http://https://sites.google.com/view/jean-jacques-herings/home

Gerard Van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Department of Econometrics and Tinbergen Institute
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Dolf J. J. Talman

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands
+31 13 466 2346 (Phone)

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