Applications of Structural Balance in Signed Social Networks

We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed social networks. A classical and major concept for signed social networks is that of structural balance, i.e., the tendency of triangles to be 'balanced' towards including an even number of negative edges, such as friend-friend-friend and friend-enemy-enemy triangles. In this article, we introduce several new signed network analysis methods that exploit structural balance for measuring partial balance, for finding communities of people based on balance, for drawing signed social networks, and for solving the problem of link prediction. Notably, the introduced methods are based on the signed graph Laplacian and on the concept of signed resistance distances. We evaluate our methods on a collection of four signed social network datasets.Comment: 37 page

SNE: Signed Network Embedding

Several network embedding models have been developed for unsigned networks. However, these models based on skip-gram cannot be applied to signed networks because they can only deal with one type of link. In this paper, we present our signed network embedding model called SNE. Our SNE adopts the log-bilinear model, uses node representations of all nodes along a given path, and further incorporates two signed-type vectors to capture the positive or negative relationship of each edge along the path. We conduct two experiments, node classification and link prediction, on both directed and undirected signed networks and compare with four baselines including a matrix factorization method and three state-of-the-art unsigned network embedding models. The experimental results demonstrate the effectiveness of our signed network embedding.Comment: To appear in PAKDD 201

Signed graph embedding: when everybody can sit closer to friends than enemies

Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions, recent empirical studies have proved that they fail to reflect some current practices in real social networks. In this paper we address the issue of drawing signed graphs and capturing such social interactions. We relax the previous assumptions to define a drawing as a model in which every vertex has to be placed closer to its neighbors connected via a positive edge than its neighbors connected via a negative edge in the resulting space. Based on this definition, we address the problem of deciding whether a given signed graph has a drawing in a given $\ell$-dimensional Euclidean space. We present forbidden patterns for signed graphs that admit the introduced definition of drawing in the Euclidean plane and line. We then focus on the $1$-dimensional case, where we provide a polynomial time algorithm that decides if a given complete signed graph has a drawing, and constructs it when applicable