Duality between equilibrium and growing networks

TL;DR

This paper demonstrates an exact equivalence between equilibrium and growing network models under certain conditions, applicable even for finite systems, bridging a fundamental gap in network theory.

Contribution

It establishes a precise, finite-size equivalence between equilibrium and growing network models, expanding the theoretical understanding of network dynamics.

Findings

Equivalence holds exactly under specific conditions.

Applicable to random geometric graphs and causal sets.

Relevant to some real-world networks.

Abstract

In statistical physics any given system can be either at an equilibrium or away from it. Networks are not an exception. Most network models can be classified as either equilibrium or growing. Here we show that under certain conditions there exists an equilibrium formulation for any growing network model, and vice versa. The equivalence between the equilibrium and nonequilibrium formulations is exact not only asymptotically, but even for any finite system size. The required conditions are satisfied in random geometric graphs in general and causal sets in particular, and to a large extent in some real networks.