1,899 research outputs found
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
MEDUSA - New Model of Internet Topology Using k-shell Decomposition
The k-shell decomposition of a random graph provides a different and more
insightful separation of the roles of the different nodes in such a graph than
does the usual analysis in terms of node degrees. We develop this approach in
order to analyze the Internet's structure at a coarse level, that of the
"Autonomous Systems" or ASes, the subnetworks out of which the Internet is
assembled. We employ new data from DIMES (see http://www.netdimes.org), a
distributed agent-based mapping effort which at present has attracted over 3800
volunteers running more than 7300 DIMES clients in over 85 countries. We
combine this data with the AS graph information available from the RouteViews
project at Univ. Oregon, and have obtained an Internet map with far more detail
than any previous effort.
The data suggests a new picture of the AS-graph structure, which
distinguishes a relatively large, redundantly connected core of nearly 100 ASes
and two components that flow data in and out from this core. One component is
fractally interconnected through peer links; the second makes direct
connections to the core only. The model which results has superficial
similarities with and important differences from the "Jellyfish" structure
proposed by Tauro et al., so we call it a "Medusa." We plan to use this picture
as a framework for measuring and extrapolating changes in the Internet's
physical structure. Our k-shell analysis may also be relevant for estimating
the function of nodes in the "scale-free" graphs extracted from other
naturally-occurring processes.Comment: 24 pages, 17 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 C 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 P(C) ~ C^δ. We find that for non-fractal scale-free networks δ = -2, and for fractal scale-free networks δ = -2 + 1/dB, where dB 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 N 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 ℓ*, separating fractal and non-fractal regimes, scales with dimension dB of the network as p−1/dB, where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p.Interfirm networks; R&D collaborations, Pharmaceutical industry; ICT.
Self-similar disk packings as model spatial scale-free networks
The network of contacts in space-filling disk packings, such as the
Apollonian packing, are examined. These networks provide an interesting example
of spatial scale-free networks, where the topology reflects the broad
distribution of disk areas. A wide variety of topological and spatial
properties of these systems are characterized. Their potential as models for
networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of
higher-dimensional packing
IMDB network revisited: unveiling fractal and modular properties from a typical small-world network
We study a subset of the movie collaboration network, imdb.com, where only
adult movies are included. We show that there are many benefits in using such a
network, which can serve as a prototype for studying social interactions. We
find that the strength of links, i.e., how many times two actors have
collaborated with each other, is an important factor that can significantly
influence the network topology. We see that when we link all actors in the same
movie with each other, the network becomes small-world, lacking a proper
modular structure. On the other hand, by imposing a threshold on the minimum
number of links two actors should have to be in our studied subset, the network
topology becomes naturally fractal. This occurs due to a large number of
meaningless links, namely, links connecting actors that did not actually
interact. We focus our analysis on the fractal and modular properties of this
resulting network, and show that the renormalization group analysis can
characterize the self-similar structure of these networks.Comment: 12 pages, 9 figures, accepted for publication in PLOS ON
Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series
A nonlinear dynamics approach can be used in order to quantify complexity in
written texts. As a first step, a one-dimensional system is examined : two
written texts by one author (Lewis Carroll) are considered, together with one
translation, into an artificial language, i.e. Esperanto are mapped into time
series. Their corresponding shuffled versions are used for obtaining a "base
line". Two different one-dimensional time series are used here: (i) one based
on word lengths (LTS), (ii) the other on word frequencies (FTS). It is shown
that the generalized Hurst exponent and the derived curves
of the original and translated texts show marked differences. The original
"texts" are far from giving a parabolic function, - in contrast to
the shuffled texts. Moreover, the Esperanto text has more extreme values. This
suggests cascade model-like, with multiscale time asymmetric features as
finally written texts. A discussion of the difference and complementarity of
mapping into a LTS or FTS is presented. The FTS curves are more
opened than the LTS onesComment: preprint for PRE; 2 columns; 10 pages; 6 (multifigures); 3 Tables; 70
reference
Statistical mechanics of complex networks
Complex networks describe a wide range of systems in nature and society, much
quoted examples including the cell, a network of chemicals linked by chemical
reactions, or the Internet, a network of routers and computers connected by
physical links. While traditionally these systems were modeled as random
graphs, it is increasingly recognized that the topology and evolution of real
networks is governed by robust organizing principles. Here we review the recent
advances in the field of complex networks, focusing on the statistical
mechanics of network topology and dynamics. After reviewing the empirical data
that motivated the recent interest in networks, we discuss the main models and
analytical tools, covering random graphs, small-world and scale-free networks,
as well as the interplay between topology and the network's robustness against
failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic
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