Phase transitions in a complex network (Q2843754)

This article approaches the study of phase transitions in complex networks, more concretely, in exponential random graphs. The authors pursue their objective employing the formalism of graphons, a useful methodology that allows the application of powerful techniques from different fields, such as mathematical analysis, in a problem which is combinatoric in origin. In particular, this formalism allows the use of large deviation theory within this context. This theory is used to prove a variational characterization of the entropy density. This variational characterization is used in turn to find graphons which are local maximizers of the entropy density. This gives some evidence of the presence of phase transitions; nevertheless, the full proof requires establishing that these maximizers are in fact global. This is postponed by the authors to a forthcoming article.