Reconstruction of a real world social network using the Potts model and Loopy Belief Propagation

• Main Authors: Cristian eBisconti, Angelo eCorallo, Laura eFortunato, Antonio Andrea Gentile, Andrea eMassafra, Piergiuseppe ePellè
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2015-11-01
• Series: Frontiers in Psychology
• Subjects: inverse problem; social network analysis; network reconstruction; quantum structures; community detection; Potts Model
• Online Access: http://journal.frontiersin.org/Journal/10.3389/fpsyg.2015.01698/full

The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, aiming at the reconstruction of a networked structure from observations of the states of the nodes in the network.The inverse Potts model, normally applied to observations of quantum states, is here addressed to observations of the node states in a network and their (anti)correlations, thus inferring interactions as links connecting the nodes. Adopting the Bethe approximation, such an inverse problem is known to be tractable.Within this operational framework, we discuss and apply this network-reconstruction method to a small real-world social network, where it is easy to track statuses of its members: the Italian parliament, adopted as a case study. The dataset is made of (co)sponsorships of law proposals by parliament members. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with standard methods, outlining discrepancies and advantages.