The random subgraph model for the analysis of an ecclesiastical network in Merovingian Gaul

In the last two decades many random graph models have been proposed to extract knowledge from networks. Most of them look for communities or, more generally, clusters of vertices with homogeneous connection profiles. While the first models focused on networks with binary edges only, extensions now allow to deal with valued networks. Recently, new models were also introduced in order to characterize connection patterns in networks through mixed memberships. This work was motivated by the need of analyzing a historical network where a partition of the vertices is given and where edges are typed. A known partition is seen as a decomposition of a network into subgraphs that we propose to model using a stochastic model with unknown latent clusters. Each subgraph has its own mixing vector and sees its vertices associated to the clusters. The vertices then connect with a probability depending on the subgraphs only, while the types of edges are assumed to be sampled from the latent clusters. A variational Bayes expectation-maximization algorithm is proposed for inference as well as a model selection criterion for the estimation of the cluster number. Experiments are carried out on simulated data to assess the approach. The proposed methodology is then applied to an ecclesiastical network in Merovingian Gaul. An R code, called Rambo, implementing the inference algorithm is available from the authors upon request.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS691 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bloggers Behavior and Emergent Communities in Blog Space

Interactions between users in cyberspace may lead to phenomena different from those observed in common social networks. Here we analyse large data sets about users and Blogs which they write and comment, mapped onto a bipartite graph. In such enlarged Blog space we trace user activity over time, which results in robust temporal patterns of user--Blog behavior and the emergence of communities. With the spectral methods applied to the projection on weighted user network we detect clusters of users related to their common interests and habits. Our results suggest that different mechanisms may play the role in the case of very popular Blogs. Our analysis makes a suitable basis for theoretical modeling of the evolution of cyber communities and for practical study of the data, in particular for an efficient search of interesting Blog clusters and further retrieval of their contents by text analysis

Local Ranking Problem on the BrowseGraph

The "Local Ranking Problem" (LRP) is related to the computation of a centrality-like rank on a local graph, where the scores of the nodes could significantly differ from the ones computed on the global graph. Previous work has studied LRP on the hyperlink graph but never on the BrowseGraph, namely a graph where nodes are webpages and edges are browsing transitions. Recently, this graph has received more and more attention in many different tasks such as ranking, prediction and recommendation. However, a web-server has only the browsing traffic performed on its pages (local BrowseGraph) and, as a consequence, the local computation can lead to estimation errors, which hinders the increasing number of applications in the state of the art. Also, although the divergence between the local and global ranks has been measured, the possibility of estimating such divergence using only local knowledge has been mainly overlooked. These aspects are of great interest for online service providers who want to: (i) gauge their ability to correctly assess the importance of their resources only based on their local knowledge, and (ii) take into account real user browsing fluxes that better capture the actual user interest than the static hyperlink network. We study the LRP problem on a BrowseGraph from a large news provider, considering as subgraphs the aggregations of browsing traces of users coming from different domains. We show that the distance between rankings can be accurately predicted based only on structural information of the local graph, being able to achieve an average rank correlation as high as 0.8