Measuring the Power of Nodes in Digraphs

Arbeitspapier

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

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 01-096/1

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General ; Game Theory and Bargaining Theory: General ; Analysis of Collective Decision-Making: General
• Subject: graph ; tournament ; power function ; Mathematische Optimierung ; Spieltheorie ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Herings, P. Jean-Jacques ; van der Laan, Gerard ; Talman, Dolf
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2001

Further information

• Handle: http://hdl.handle.net/10419/86107
• Last update: 10.03.2025, 11:42 AM CET