Transitivity Model on Signed Graphs

In this paper, we generalize the already established iterated local transitivity model for online social networks in signed networks. In this model, at each time step t and for already existing vertex x, a new vertex(clone) x′ is added which joins to the neighbors of x. The sign of new edge xx′ is the marking on x. We also discuss the properties such as balance, clusterability, sign-compatibility and consistency. The signed networks focus on the type of relations (friendship and enmity) between the vertices(members of online social network). The ILT model for signed network gives an insight on how the network reacts to the addition of clone vertex. Also the properties like balance and clusterability helps establish a natural balance in society by providing a possible formation of group of vertices in society for a peaceful co-existence and smooth functioning of social system.