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The importance of trust in social networks instigated many research efforts to understand it and predict it. However, the complex nature of trust and its counterpart; distrust; makes these tasks challenging. While early trust inference approaches ignore distrust, it seems that this concept gained much attention in recent years. Surely, knowing whom to distrust is as important as knowing whom to trust. We show in this paper that trust and distrust can be quickly predicted using some social traits of the trustor and the trustee. Using a "tug of war" analogy involving these traits, we have devised an intuitive approach that uses only the direct neighbors of the trustor and those of the trustee to predict both trust and distrust. Experiments on four real-world social networks show that our algorithm is very fast, provides good predictions, and is robust to network sparsity.

Trust is a very significant notion in social life, and even more in online social networks where people from different cultures and backgrounds interact. Weighted Signed Networks (WSNs) are an elegant representation of social networks, since they are able to encode both positive and negative relations, thus allow to express trust and distrust as we know them in the real world. While many trust inference algorithms exist for traditional unsigned networks, distrust makes it hard to adapt them to WSNs. In this paper, we propose a new unsupervised trust inference algorithm based on collaborative filtering (CF), where we consider the trustors as users, the trustees as items, and use agreement as a local similarity metric to predict trust values in signed, and unsigned, networks. In addition to its prediction performances, experiments on four real-world datasets show that our algorithm is very robust to network sparsity.

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In practice, an alliance can be a bond or connection between individuals, families, states, or entities, etc. Formally, a non-empty set S of vertices of a graph G is a defensive k-alliance (resp. an offensive k-alliance) if every vertex of S (resp. the boundary of S) has at least k more neighbors inside of S than it has outside of S. A powerful k-alliance is both defensive k-alliance and offensive (k+2)alliance. During the last decade there has been a remarkable development on these three kinds of alliances. Due to their variety of applications, the alliances in its broad sense have received a special attention from many scientists and researchers. There have been applications of alliances in several areas such as bioinformatics, distributed computing, web communities, social networks, data clustering, business, etc. Several k-alliance numbers have been defined and a huge number of theoretical (algorithmic and computational) results are obtained for various graph classes. In this paper, we present a survey which covers a number of practical applications of alliances and the vast mathematical properties of the three types of k-alliances by giving a special attention to the study of the associated k-alliance (partition) numbers for different graph classes. c