Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation

Abstract

The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, for the reconstruction of the structure of a social network. The inverse Potts model, traditionally applied to recursive observations of quantum states in an ensemble of particles, is here addressed to observations of the members' states in an organization and their (anti)correlations, thus inferring interactions as links among the members. Adopting proper (Bethe) approximations, such an inverse problem is showed to be tractable. Within an operational framework, this network-reconstruction method is tested for a small real-world social network, the Italian parliament. In this study case, it is easy to track statuses of the parliament members, using (co)sponsorships of law proposals as the initial dataset. 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 such standard methods, outlining discrepancies and advantages.

The Tightness of the Kesten–Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations

“…For example, our model and the construction threshold can be used to effectively identify community effect in social networks and customer loyalty in marketing research, especially for different firms or organizations who want to promote their products or philosophies. In this sense, many possible extensions can be made on research on graph structures with psychological factors involved, such as the work by Liu, Ying and Shakkottai [24] on Ising model based analysis on the formation and propagation of opinions across networks, the work by Bisconti et al [6] on Potts model based analysis on the reconstruction of a real world social network and loopy belief propagation, etc.…”

Multiple metastable states in an off-lattice Potts model

“…Spin models, such as the Ising model and its generalization, the Potts model [1], have been proposed to describe correlation between individual sites, in different fields of Science including condensed matter physics [2], neuroscience [3], social science [4], percolation theory [5], among many others.…”

Statistical mechanics approach for collaborative business social network reconstruction

“…However, if the direct application of these models has been widely explored, the inverse problem formulation is mostly confined to the Ising model alone, and most of its interest for non-physical problems has involved so far only biological and neural sciences (Ricci-Tersenghi 2012; Yamanishi et al 2004), or image reconstruction tasks (Kiwata 2012). To authors' knowledge, this paper (along with Bisconti et al 2015) is the first one using the inverse Potts problem to reconstruct a network in social sciences, and it is in general the first to apply a moment-based loopy belief propagation (LBP) method 1 to solve the Potts inverse problem in the real world.…”