We study the structure of online discussions in order to uncover latent communities of socially important debate. Our research reveals that discussion communities defined by mutual commenting in the Russian language blogosphere are centered mainly around blog authors as opinion leaders and, to a lesser extent, around a shared topic or topics. We have derived these conclusions from the dataset of 17386 full text posts written by top 2000 LiveJournal bloggers and over 520,000 comments that result in about 4.5 million edges in the network of co-commenting.JEL classification: Z19.

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Abstract. We propose a probabilistic model for learning continuous vector representations of nodes in directed networks. These representations could be used as high quality features describing nodes in a graph and implicitly encoding global network structure. The usefulness of the representations is demonstrated on link prediction and graph visualization tasks. Using representations learned by our method allows to obtain results comparable to state of the art methods on link prediction while requires much less computational resources. We develop an efficient online learning algorithm which makes it possible to learn representations from large and non-stationary graphs. It takes less than a day on a commodity computer to learn high quality vectors on LiveJournal friendship graph consisting of 4.8 million nodes and 68 million links and the reasonable quality of representations can be obtained much faster.