SpecialityUniversity of Siena, IT

Statistical Mechanics of temporal networks, with empirical applicationsMany of the social, financial and man-made networks around us are inherently complex, displaying non-trivial linkage patterns, and dynamic, with their links switching on and off over time. Maximum-entropy graph ensembles have proven to be extremely useful for the statistical description of real-world networked systems in a static framework. The evolution of such systems is often observed to be complex as well, characterized by many persistence patterns that coexist in time, non-Markovian memory or even non stationary effects, and correlated dynamics for the links. Here, it is shown how maximum-entropy graph ensembles are effective to describe dynamical patterns for temporal networks and the equivalence (under some conditions) to discrete autoregressive processes. A new general class of models of temporal networks is then introduced in order to solve a number of problems: (i) predicting the evolution of networks; (ii) disentangling the link formation mechanisms in empirical networks; (iii) understanding how information and other relevant quantities propagate over networks in the presence of temporal effects.