Information super-diffusion on structured networks

Abstract

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by powerlaws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.

Local Information Based Algorithms for Packet Transport in Complex Networks

“…We have demonstrated comparatively how these algorithms work in traffic on an uncorrelated scale-free network, which is known to be very prone for jamming [5]. These are the algorithms STD and CDT, which are based on the updated statistics of the travel times of packets (global information) and (local) information on the degree of their nearest neighbour nodes.…”

“…Thus our model falls within the Network Layer of the OSI Reference Model and the algorithms described in section 3 are routing algorithms that belong to the Network Layer of the OSI Reference Model. Of particular interest is the phenomenon of load in a network, as a function of the rate of packet creation R, which has been investigated for models of communication networks [5,6], [7], [8] and in real networks [9].…”

Complex Network of Earthquakes

“…Relevance of Tsallis nonextensive statistical mechanics [10]- [15] to a complex networks has recently been a noticed also in [29].…”

Guided Search and Distribution of Information Flow on Complex Graphs

“…The inhomogeneity and sparseness of complex networks effect dynamic processes that these networks support. Recent study of traffic on networks of diverse emergent topologies [1,5] revels that functional efficiency of a network, however, is not determined by the network's topology alone, but it also depends on the microscopic rules of the dynamics. In particular, in the transport processes on networks the rules which are adapted to the locally changing networks' structure lead to more efficient network performance.…”

“…Within the numerical model proposed in [1] we study the flow of information on a graph with power-law organization of links and an emergent superstructure formed by two highly interconnected hubs. The local search algorithms which navigate transport at each node can use information in the range of zero, one, and two-nearest neighbourhood of the node.…”