Analysing Asymmetrical Associations using Fuzzy Graph and Discovering Hidden Connections in Facebook

Abstract

The fuzzy graph theory to analyse the relationship strength in Social Networks has gain significant potential in last few years and has seen applications in areas like Link Prediction, calculating Reciprocity, discovering central nodes etc. In this paper, we propose a framework to analyse and quantify the degree of strength of asymmetric relationships and predict hidden links in social networks using fuzzy logic. Till now, the work in fuzzy social relational networks has been limited to symmetric relationships. However, in this paper, we consider the scenario of asymmetric relations. The proposed approach is for web 2.0 application <em>Facebook</em>. Our contribution is three fold. First, the measurement of the strength of asymmetric relationship between nodes on the basis of social interaction using the concept of fuzzy graph. Second, a hybrid approach for prediction of missing links between two nodes on the basis of similarity of attributes of user profiles such as demographic, topology and network transactional data. Third, we perform fuzzy granular computing on attribute ‘strength of relationship’ and categorise into four granules namely <em>{socially close friends, socially near friends, socially far friends, socially very far friends}</em> based on the results of supervised learning conducted over dataset. Similarly, actual outcome for predicted links is categorised into three granules namely <em>Accept, Not accept and May be.</em> The proposed approach has predicted relationship strength with mean absolute error of 9.26% whereas the proposed approach for Link prediction has provided 64% correct predictions.