Discovering Influential Nodes for SIS models in Social Networks Kazumi Saito 1 , Masahiro Kimura 2 , and Hiroshi Motoda 3 1 School of Administration and Informatics, University of Shizuoka 52-1 Yada, Suruga-ku, Shizuoka 422-8526, Japan k-saito@u-shizuoka-ken.ac.jp 2 Department of Electronics and Informatics, Ryukoku University Otsu, Shiga 520-2194, Japan kimura@rins.ryukoku.ac.jp 3 Institute of Scientific and Industrial Research, Osaka University 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan motoda@ar.sanken.osaka-u.ac.jp Abstract. We address the problem of efficiently discovering the influential nodes in a social network under the susceptible/infected/susceptible (SIS) model, a diffu- sion model where nodes are allowed to be activated multiple times. The compu- tational complexity drastically increases because of this multiple activation prop- erty. We solve this problem by constructing a layered graph from the original social network with each layer added on top as the time proceeds, and apply- ing the bond percolation with pruning and burnout strategies. We experimentally demonstrate that the proposed method gives much better solutions than the con- ventional methods that are solely based on the notion of centrality for social net- work analysis using two large-scale real-world networks (a blog network and a wikipedia network). We further show that the computational complexity of the proposed method is much smaller than the conventional naive probabilistic sim- ulation method by a theoretical analysis and confirm this by experimentation. The properties of the influential nodes discovered are substantially different from those identified by the centrality-based heuristic methods. 1 Introduction Social networks mediate the spread of various information including topics, ideas and even (computer) viruses. The proliferation of emails, blogs and social networking ser- vices (SNS) in the World Wide Web accelerates the creation of large social networks. Therefore, substantial attention has recently been directed to investigating information diffusion phenomena in social networks [1–3]. Overall, finding influential nodes is one of the most central problems in social net- work analysis. Thus, developing methods to do this on the basis of information diffusion is an important research issue. Widely-used fundamental probabilistic models of infor- mation diffusion are the independent cascade (IC) model and the linear threshold (LT) model [4, 5]. Researchers investigated the problem of finding a limited number of influ- ential nodes that are effective for the spread of information under the above models [4,