3,978 research outputs found

    Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops

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    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=3k=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.Comment: 14 pages, 5 figure

    KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation

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    We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies on two new theoretical contributions, of independent interest. The first contribution focuses on sampling shortest paths, a subroutine used by most algorithms that approximate betweenness centrality. We show that, on realistic random graph models, we can perform this task in time ∣E∣12+o(1)|E|^{\frac{1}{2}+o(1)} with high probability, obtaining a significant speedup with respect to the Θ(∣E∣)\Theta(|E|) worst-case performance. We experimentally show that this new technique achieves similar speedups on real-world complex networks, as well. The second contribution is a new rigorous application of the adaptive sampling technique. This approach decreases the total number of shortest paths that need to be sampled to compute all betweenness centralities with a given absolute error, and it also handles more general problems, such as computing the kk most central nodes. Furthermore, our analysis is general, and it might be extended to other settings.Comment: Some typos correcte

    Transport on complex networks: Flow, jamming and optimization

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    Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics

    Numerical Investigation of Metrics for Epidemic Processes on Graphs

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    This study develops the epidemic hitting time (EHT) metric on graphs measuring the expected time an epidemic starting at node aa in a fully susceptible network takes to propagate and reach node bb. An associated EHT centrality measure is then compared to degree, betweenness, spectral, and effective resistance centrality measures through exhaustive numerical simulations on several real-world network data-sets. We find two surprising observations: first, EHT centrality is highly correlated with effective resistance centrality; second, the EHT centrality measure is much more delocalized compared to degree and spectral centrality, highlighting the role of peripheral nodes in epidemic spreading on graphs.Comment: 6 pages, 1 figure, 3 tables, In Proceedings of 2015 Asilomar Conference on Signals, Systems, and Computer
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