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We define a minimal model of traffic flows in complex networks containing the most relevant features of real routing schemes, i.e. a trade--off strategy between topological-based and traffic-based routing. The resulting collective behavior, obtained analytically for the ensemble of uncorrelated networks, is physically very rich and reproduces results recently observed in traffic simulations on scale-free networks. We find that traffic control is useless in homogeneous graphs but may improves global performance in inhomogeneous networks, enlarging the free-flow region in parameter space. Traffic control also introduces non-linear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner.
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researche
In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose a method t
Cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. Focusing on cycle structure, this paper defines a new matrix, named cycle number matrix, to represent cycle information of a
A model of communication that is able to cope simultaneously with the problems of search and congestion is presented. We investigate the communication dynamics in model networks and introduce a general framework that enables a search of optimal structures.
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a cascading way and