Social boundary of any two nodes in a social network

It is generally accepted that the driving forces of establishing connections among people are social influence and homophily. Both of them eventually lead to the proximity of any two related individuals to some extent. However, a person always can be featured with some attributes different from his/her social networking partners. Accordingly, one person´s direct and indirect social relationships are likely to intersect with others at some nodes in social networks. In this work, we study the novel task of identifying the hidden boundary that divides the social network into disjoint social circles according to any pair of nodes which we call social boundary. We put forward two methods to separate the social circles of any two nodes and thus can find out the social boundary. One is based on label propagation and the other is based on perceptron network model. We apply the methods on synthetic and real networks, respectively. Finally, we demonstrate the areas in which it would be applied.