3,704 research outputs found
Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops
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 . 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
Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks
We study the betweenness centrality of fractal and non-fractal scale-free
network models as well as real networks. We show that the correlation between
degree and betweenness centrality of nodes is much weaker in fractal
network models compared to non-fractal models. We also show that nodes of both
fractal and non-fractal scale-free networks have power law betweenness
centrality distribution . We find that for non-fractal
scale-free networks , and for fractal scale-free networks , where is the dimension of the fractal network. We support
these results by explicit calculations on four real networks: pharmaceutical
firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network
at AS level (N=20566), where is the number of nodes in the largest
connected component of a network. We also study the crossover phenomenon from
fractal to non-fractal networks upon adding random edges to a fractal network.
We show that the crossover length , separating fractal and
non-fractal regimes, scales with dimension of the network as
, where is the density of random edges added to the network.
We find that the correlation between degree and betweenness centrality
increases with .Comment: 19 pages, 6 figures. Submitted to PR
Predicting Scientific Success Based on Coauthorship Networks
We address the question to what extent the success of scientific articles is
due to social influence. Analyzing a data set of over 100000 publications from
the field of Computer Science, we study how centrality in the coauthorship
network differs between authors who have highly cited papers and those who do
not. We further show that a machine learning classifier, based only on
coauthorship network centrality measures at time of publication, is able to
predict with high precision whether an article will be highly cited five years
after publication. By this we provide quantitative insight into the social
dimension of scientific publishing - challenging the perception of citations as
an objective, socially unbiased measure of scientific success.Comment: 21 pages, 2 figures, incl. Supplementary Materia
Betweenness Centrality in Large Complex Networks
We analyze the betweenness centrality (BC) of nodes in large complex
networks. In general, the BC is increasing with connectivity as a power law
with an exponent . We find that for trees or networks with a small loop
density while a larger density of loops leads to . For
scale-free networks characterized by an exponent which describes the
connectivity distribution decay, the BC is also distributed according to a
power law with a non universal exponent . We show that this exponent
must satisfy the exact bound . If the scale
free network is a tree, then we have the equality .Comment: 6 pages, 5 figures, revised versio
Optimal Traffic Networks
Inspired by studies on the airports' network and the physical Internet, we
propose a general model of weighted networks via an optimization principle. The
topology of the optimal network turns out to be a spanning tree that minimizes
a combination of topological and metric quantities. It is characterized by a
strongly heterogeneous traffic, non-trivial correlations between distance and
traffic and a broadly distributed centrality. A clear spatial hierarchical
organization, with local hubs distributing traffic in smaller regions, emerges
as a result of the optimization. Varying the parameters of the cost function,
different classes of trees are recovered, including in particular the minimum
spanning tree and the shortest path tree. These results suggest that a
variational approach represents an alternative and possibly very meaningful
path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio
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