Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops

Abstract

We consider the role of network geometry in two types of diffusion processes: transport of constant-density information packets with queuing on nodes, and constant voltage-driven tunneling of electrons. The underlying network is a homogeneous graph with scale-free distribution of loops, which is constrained to a planar geometry and fixed node connectivity $k=3$. We determine properties of noise, flow and return-times statistics for both processes on this graph and relate the observed differences to the microscopic process details. Our main findings are: (i) Through the local interaction between packets queuing at the same node, long-range correlations build up in traffic streams, which are practically absent in the case of electron transport; (ii) Noise fluctuations in the number of packets and in the number of tunnelings recorded at each node appear to obey the scaling laws in two distinct universality classes; (iii) The topological inhomogeneity of betweenness plays the key role in the occurrence of broad distributions of return times and in the dynamic flow. The maximum-flow spanning trees are characteristic for each process type.

14 pages, 5 figures

References in corpus (1)

• Topology of Cell-Aggregated Planar Graphs

Cited by in corpus (6)

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• Transport on Complex Networks: Flow, Jamming and Optimization
• The effect of bandwidth in scale-free network traffic
• Preferential Behaviour and Scaling in Diffusive Dynamics on Networks
• Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
• Queue-length synchronization in a communication networks