Coarse-grained topology estimation via graph sampling

In many online networks, nodes are partitioned into categories (e.g., countries or universities in OSNs), which naturally defines a weighted category graph i.e., a coarse-grained version of the underlying network. In this paper, we show how to efficiently estimate the category graph from a probability sample of nodes. We prove consistency of our estimators and evaluate their efficiency via simulation. We also apply our methodology to a sample of Facebook users to obtain a number of category graphs, such as the college friendship graph and the country friendship graph. We share and visualize the resulting data at www.geosocialmap.com.