Designing and Connectivity Checking of Implicit Social Networks from the User-Item Rating Data

\\emph{Implicit Social Network} is a connected social structure among a group\nof persons, where two of them are linked if they have some common interest. One\nreal\\mbox{-}life example of such networks is the implicit social network among\nthe customers of an online commercial house, where there exists an edge between\ntwo customers if they like similar items. Such networks are often useful for\ndifferent commercial applications such as \\textit{target advertisement},\n\\textit{viral marketing}, etc. In this article, we study two fundamental\nproblems in this direction. The first one is that, given the user\\mbox{-}item\nrating data of an E\\mbox{-}Commerce house, how we can design implicit social\nnetworks among its users and the second one is at the time of designing itself\ncan we obtain the connectivity information among the users. Formally, we call\nthe first problem as the \\textsc{Implicit User Network Design} Problem and the\nsecond one as \\textsc{Implicit User Network Design with Connectivity Checking}\nProblem. For the first problem, we propose three different algorithms, namely\n\\emph{`Exhaustive Search Approach'}, \\emph{`Clique Addition Approach'}, and\n\\textit{`Matrix Multiplication\\mbox{-}Based Approach'}. For the second problem,\nwe propose two different approaches. The first one is the sequential approach:\ndesigning and then connectivity checking, and the other one is a concurrent\napproach, which is basically an incremental algorithm that performs designing\nand connectivity checking simultaneously. Proposed methodologies have\nexperimented with three publicly available rating network datasets such as\n\\emph{Flixter}, \\textit{Movielens}, and \\textit{Epinions}.\n