On the complexity of cooperative solution concepts
Mathematics of Operations Research
Introduction to Algorithms
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
Determining the top-k nodes in social networks using the Shapley value
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 3
Influential nodes in a diffusion model for social networks
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A shapley value approach for influence attribution
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
A new approach to betweenness centrality based on the Shapley Value
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Using coalitional games to detect communities in social networks
WAIM'13 Proceedings of the 14th international conference on Web-Age Information Management
A game theory based approach for community detection in social networks
BNCOD'13 Proceedings of the 29th British National conference on Big Data
Optimum profit allocation in coalitional VoD service
Computer Networks: The International Journal of Computer and Telecommunications Networking
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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.