On Measurement of Influence in Social Networks Behnam Hajian School of Computer Science Carleton University, Ottawa, Canada Email: bhajian@scs.carleton.ca Tony White School of Computer Science Carleton University, Ottawa, Canada Email: arpwhite@scs.carleton.ca Abstract—One of the issues to be resolved in social rec- ommender systems is the identification of opinion leaders in a network. Finding effective people in societies has been a key question for many groups; e.g., marketers. The research undertaken in this paper focuses on finding important nodes in a network based on their behaviour as well as the structure of the network. This paper views the propagation of information in a social network as a process of infection. The paper proposes an algorithm called the Probability Propagation Method for measuring the probability of infection of all the nodes in a network starting from a given node in the network. Then, assuming independence in activation of nodes in a network, a method is proposed for ranking nodes according to their capabilities in infecting a larger number of nodes in a network. These methods are validated using simulation software in which a non-deterministic model of information diffusion is simulated on several classes of network. I. I NTRODUCTION On-line recommender systems are disregarded or ignored by their users generally because their users feel suggestions from these systems are useless [1]. It has been proven that the main reason for this feeling is that people prefer to get recommendations from the people they trust rather than automated advertising software [2]. On the one hand, these systems are incapable of recognizing their users’ needs in a timely manner due to the lack of information about their life and, on the other hand, these systems suffer from a lack of knowledge about the users’ interests [3]. The former problem has not been studied extensively and the latter is generally called the Cold Start Problem [1] in the on-line recommender system literature. According to Iyengar et al. [4], friends have a significant effect on the purchase probability of a customer for a specific product. These researchers discovered that the social effect is zero for 48% of social network users, negative for 12% of the users and positive for 40% of the users. On the one hand, imitation is also effective in increasing revenue and sales, while users tend to buy some of the new products when their friends already bought that product. On the other hand, sometimes this fact has a negative effect, since some users are reluctant to buy a product which has already been bought by their friends. A. Motivation and Problem Statement Adaptability to innovations and new products is another issue for marketing cutting edge products. However, it has been observed that people are infected by a new idea from being exposed to the innovation by their friends, rather than advertisements. This fact motivates marketers to turn to viral marketing rather than ad-hoc advertising. It is clear that influ- ence varies from node to node in a network and identifying the most influential nodes can significantly affect the effectiveness of an advertising campaign. It is this problem that motivates the research reported in this paper. This paper focuses on how to rank nodes according to their ability to infect more nodes if that node individually gets infected. This problem is referred to in this paper as the influence measurement problem because influence is modelled as the ability of a node to infect other nodes in the network. A related category of problems is one in which a set of nodes of a given size, k, is constructed which maximizes the number of infected nodes in a network. We refer to this problem as the k set influence maximization problem. The question in this paper focuses on the effect of each individual on the infection of nodes in the network. However, in the other problem category, the influence of an individual is not important by itself, but we focus on the combination of nodes in a set and we expect an increasing number of infected nodes when adding a new node to the set. In the second problem, we have to consider overlaps among sets of infected nodes. In other words, while we try to find the node with the maximum number of infections, the overlap between the new set and the set of already infected nodes has to be minimized. The second problem is outside of the scope of this paper. The remainder of this paper is organized in five sections. Section two describes related work. In Section three, a model of information diffusion is proposed in the context of a social network. Section four provides proposed algorithms for measuring influence in a social network. In order to validate the proposed algorithms, a general framework of a social network is simulated. Section five discusses the properties of our simulations, experimental results and includes a discussion of the results. Finally, conclusions and future work will be discussed in Section six. II. RELATED WORK There exist several methods for measuring importance of nodes in a network; such as: Closeness, Betweenness, and Eigenvector centrality measures. Simply put, these metrics concentrate on the structure of the network rather than the behavior of nodes and their interactions. However, researchers have also considered other aspects of analysis, such as analysis