Bayesian inference of private social network links using prior information and propagated data

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Inferring network structure has many applications ranging from viral marketing to privacy forensics, infection prevention and information feed ranking. In complex or social networks some agents or users tend to keep their connections hidden. The main focus of this research is inferring hidden and invisible network connections through the data collected from propagations or cascades with the help of some other rich information e.g. comments, profile information, joint photos or interactions of users. We analyze the information propagation mechanism based on a two-phase algorithm. Traversing the first phase relies on using the social network data set in order to estimate the friendship probability among its users. Performing this procedure would result in generating a primitive friendship graph which includes the probability of every two users being effectively connected. The propagation times of one or more cascades are fed into a Maximum A Posteriori (MAP) estimator to find the active hidden links using a Bayesian inference method. The algorithm was evaluated on a real network graph extracted from part of Facebook. Mutual friendships were used as the prior information for test purposes. The results showed that it is possible to achieve very high accuracy with limited cascades if the ratio of the nodes with hidden friends is not high.