Adhesion-induced Discontinuous Transitions and Classifying Social Networks

TL;DR

This paper uncovers a new class of discontinuous phase transitions in network restructuring driven by adhesion, revealing distinct phases with different degree distribution characteristics in both theoretical models and social networks.

Contribution

It introduces a novel class of intrinsically discontinuous transitions in non-growing networks caused by adhesion, supported by an analytic master equation solution.

Findings

Discontinuous transitions separate phases with monotonic and peaked degree distributions.

Analytic solution of the master equation characterizes the transition.

Empirical data shows similar phase separation in social networks.

Abstract

Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network growth processes. Real networks not only grow but often also restructure, yet common network restructuring processes, such as small world rewiring, do not exhibit phase transitions. Here, we uncover a class of intrinsically discontinuous transitions emerging in network restructuring processes controlled by \emph{adhesion} -- the preference of a chosen link to remain connected to its end node. Deriving a master equation for the temporal network evolution and working out an analytic solution, we identify genuinely discontinuous transitions in non-growing networks, separating qualitatively distinct phases with monotonic and with peaked degree distributions. Intriguingly, our analysis of heuristic data indicates a separation between the same two forms of degree distributions distinguishing abstract from face-to-face social networks.