TR-11-09: Modelling Influence in a Social Network: Metrics and evaluation

Abstract

Social recommender systems are a recently introduced type of decision support system. One of the issues to be resolved in social recommender systems is the identification of opinion leaders in a network. Social Network Analysis is generally known for measuring network location metrics, centrality of nodes, and accessibility of users to one another in a network. While these measures are important in providing insight for defining roles in networks or defining different communities in a network, such measures miss important behavioral aspects of the network. The focus of this paper is the analysis of a network based on the interactions between users called behavioral analysis. One such measure is Influence Rank. The hypothesis explored in this paper is that this rank can be quantified based on the interaction between users and their behavior. The Influence Rank for a node is defined as the average Influence Rank of its neighborhoods combined with another index called Magnitude of Influence. The correlation between the proposed indices is analyzed in this paper. This combined measure is calculated by a recursive formula whose calculation complexity in the worst case yields non-polynomial time. However, this measure can be estimated by using the PageRank algorithm. The algorithm proposed here is based on estimating PageRank by eigenvector which is compared with an algorithm based on the limited iteration by depth of a spanning tree of the network. Results supporting the utility of the measure and the accuracy of its estimation using the PageRank approximation are presented. Keywords- Social Influence; Social Network; Modeling; Behavioural Analysis

TR-11-09.pdf