2005/09/09 by A. G. Angel, A G Angel, T. Hanney +1 · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Combinatorics #Complex Network Analysis Techniques #Computer science #Condensation #Fraction (chemistry) #Lattice (music) #Materials science #Mathematics #Network model #Node (physics) #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Range (aeronautics) #Statistical physics #Theoretical and Computational Physics #Thermodynamics #Zero (linguistics) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.73.016105
published as Phys. Rev. E 73, 016105 (2006) · 23 pages, 8 figures
arxiv created 2005/09/09 · openalex publication_date 2006/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total out-strength condenses onto a single link; (ii) a phase in which a finite fraction of the total weight in the system is directed into a single node. A virtue of the model is that its dynamics can be mapped onto those of a zero-range process with many species of interacting particles--an exactly solvable model of particles hopping between the sites of a lattice. This mapping, which is described in detail, guides the analysis of the steady state of the network model and leads to theoretical predictions for the conditions under which the different types of condensation may be observed. A further advantage of the mapping is that, by exploiting what is known about exactly solvable generalizations of the zero-range process, one can infer a number of generalizations of the network model and dynamics which remain exactly solvable.