Inversion method for content-based networks

In this paper, we generalize a recently introduced expectation maximization (EM) method for graphs and apply it to content-based networks. The EM method provides a classification of the nodes of a graph, and allows one to infer relations between the different classes. Content-based networks are ideal models for graphs displaying any kind of community and/or multipartite structure. We show both numerically and analytically that the generalized EM method is able to recover the process that led to the generation of such networks. We also investigate the conditions under which our generalized EM method can recover the underlying content-based structure in the presence of randomness in the connections. Two entropies, S-q and S-c, are defined to measure the quality of the node classification and to what extent the connectivity of a given network is content based. Sq and Sc are also useful in determining the number of classes for which the classification is optimal.