Communication in networks with hierarchical branching.

By Alex Arenas, Albert Díaz-Guilera, R. I. Virgili, U. Barcelona. Physical Review Letters, 2000

353 citations recorded by the source corpus.

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/38e92d3aa46b2656fc87f892ace85be9875092e0

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The “New” Science of Networks (2004, background): “…1999), mathematical epidemiologists have preferred to develop modeling approaches that assume individuals within any given population mix randomly (Anderson & May 1991, Bailey The basic model of disease spread, introduced by Kermack & McKendrick…”
The structure and dynamics of multilayer networks (2014, background): “As congestion results in the unbalance between the number of packets introduced in the network and that of delivered ones, the following order parameter [220,221]”
Modelling dynamical processes in complex socio-technical systems (2011, background): “In the case of packet-traffic routing, homogeneous networks have typically much larger congestion thresholds than heterogeneous graphs 67–69 .”
Critical phenomena in complex networks (2007, background): “[Similar critical effects were found in an analytically treatable model of traffic in networks with hierarchical branching, see Arenas et al. (2001).] They proposed the following idea. Since the traffic is most efficient at λc, the Internet self-organizes to operate at criticality. This results in v”