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Efficient Computation of the Shapley Value for Centrality in Networks

Efficient Computation of the Shapley Value for Centrality in Networks
Efficient Computation of the Shapley Value for Centrality in Networks
The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is of paramount significance in many real-world application domains including social and organisational networks, biological networks, communication networks and the internet. Whereas computational aspects of the Shapley Value have been analyzed in the context of conventional coalitional games, this paper presents the first such study of the Shapley Value for network centrality. Our results demonstrate that this particular application of the Shapley Value presents unique opportunities for efficiency gains, which we exploit to develop exact analytical formulas for Shapley Value based centrality computation in both weighted and unweighted networks. These formulas not only yield efficient (polynomial time) and error-free algorithms for computing node centralities, but their surprisingly simple closed form expressions also offer intuition into why certain nodes are relatively more important to a network.
1-13
Aadithya, Karthik V.
31134f62-1297-4f77-8d22-cd1361fa1dd2
Ravindran, Balaraman
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Michalak, Tomasz P.
e24bfee3-bd75-4cca-8220-6f3c2f39dc38
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Aadithya, Karthik V.
31134f62-1297-4f77-8d22-cd1361fa1dd2
Ravindran, Balaraman
090725cb-f627-4ed7-9a03-a1aa13086aa3
Michalak, Tomasz P.
e24bfee3-bd75-4cca-8220-6f3c2f39dc38
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Aadithya, Karthik V., Ravindran, Balaraman, Michalak, Tomasz P. and Jennings, Nicholas R. (2010) Efficient Computation of the Shapley Value for Centrality in Networks. Proc. 6th Int Workshop on Internet and Network Economics (WINE-2010), Stanford University, Stanford, California, United States. 13 - 17 Dec 2010. pp. 1-13 .

Record type: Conference or Workshop Item (Paper)

Abstract

The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is of paramount significance in many real-world application domains including social and organisational networks, biological networks, communication networks and the internet. Whereas computational aspects of the Shapley Value have been analyzed in the context of conventional coalitional games, this paper presents the first such study of the Shapley Value for network centrality. Our results demonstrate that this particular application of the Shapley Value presents unique opportunities for efficiency gains, which we exploit to develop exact analytical formulas for Shapley Value based centrality computation in both weighted and unweighted networks. These formulas not only yield efficient (polynomial time) and error-free algorithms for computing node centralities, but their surprisingly simple closed form expressions also offer intuition into why certain nodes are relatively more important to a network.

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More information

Published date: 5 October 2010
Additional Information: Event Dates: 13-18 December 2010
Venue - Dates: Proc. 6th Int Workshop on Internet and Network Economics (WINE-2010), Stanford University, Stanford, California, United States, 2010-12-13 - 2010-12-17
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 271617
URI: http://eprints.soton.ac.uk/id/eprint/271617
PURE UUID: cee4a883-ca38-4662-85a0-0372d6f5d321

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Date deposited: 06 Oct 2010 08:15
Last modified: 14 Mar 2024 09:35

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Contributors

Author: Karthik V. Aadithya
Author: Balaraman Ravindran
Author: Tomasz P. Michalak
Author: Nicholas R. Jennings

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