Communication in networks with hierarchical branching
  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. Despite the simplicity of the model, the analytical results are a useful guide to forecast the main features of real networks. 
A. Arenas (1), A. Diaz-Guilera (2), R. Guimera (1) ((1) Universitat   Rovira i Virgili, (2) Universitat de Barcelona)