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
Mobile agent-based approach for modeling the epidemics of communicable diseases
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
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The concept of centrality plays an important role in network analysis. Game theoretic centrality measures have been recently proposed, which are based on computing the Shapley Value (SV) of each node (agent) in a suitably constructed co-operative network game (for example see [1]). However, the naive method of exact computation of SVs takes exponential time in the number of nodes. In this paper, we develop analytical formulas for computing SVs of nodes for various kinds of centrality-related co-operative games played on both weighted and unweighted networks. These formulas not only provide an efficient and error-free way of computing node centralities, but their surprisingly simple closed form expressions also offer intuition into why certain nodes are relatively more important to a network.