Duality between equilibrium and growing networks
arXiv:1302.3530 · doi:10.1103/PhysRevE.88.022808
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.
References in corpus (9)
- Hyperbolic Geometry of Complex Networks
- The entropy of randomized network ensembles
- On dynamic network entropy in cancer
- Efficient and exact sampling of simple graphs with given arbitrary degree sequence
- Generalized Bose-Fermi statistics and structural correlations in weighted networks
- Network Cosmology
- Entropy of dynamical social networks
- The structure of causal sets
- Clustering of random scale-free networks
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