Estimating Network Structure from Anonymous Ego-centric Information

Abstract

We address a problem of estimating the whole structure of an actual social network of people from only their two types of anonymous ego-centric information, personal attributes like sex and relational ones like the numbers of female and male friends, obtained as answers to questionnaires in a social survey. From these attribute values, we can obtain the degree of each node, which corresponds to the number of friends of each person, together with some macroscopic information about the network, like the ratio of links between female and male nodes to the total number of links, as the mixing matrices. However, we cannot directly know the actual connections between two nodes only from these observed mixing matrices. Thus, we propose a new method for estimating the whole structure of the hidden network by minimizing the Kullback-Leibler divergence between each pair of the observed and estimated mixing matrices, under the constraints with respect to the degree of each node. In our experiments using three types of networks, we show that the proposed method can produce much better estimation results, in comparison to a random baseline which is assigned arbitrary links under the degree constraints, especially for the cases of highly assortative, where each node has a tendency to connect to nodes with the same attribute values.