542 research outputs found
The Blind Watchmaker Network: Scale-freeness and Evolution
It is suggested that the degree distribution for networks of the
cell-metabolism for simple organisms reflects an ubiquitous randomness. This
implies that natural selection has exerted no or very little pressure on the
network degree distribution during evolution. The corresponding random network,
here termed the blind watchmaker network has a power-law degree distribution
with an exponent gamma >= 2. It is random with respect to a complete set of
network states characterized by a description of which links are attached to a
node as well as a time-ordering of these links. No a priory assumption of any
growth mechanism or evolution process is made. It is found that the degree
distribution of the blind watchmaker network agrees very precisely with that of
the metabolic networks. This implies that the evolutionary pathway of the
cell-metabolism, when projected onto a metabolic network representation, has
remained statistically random with respect to a complete set of network states.
This suggests that even a biological system, which due to natural selection has
developed an enormous specificity like the cellular metabolism, nevertheless
can, at the same time, display well defined characteristics emanating from the
ubiquitous inherent random element of Darwinian evolution. The fact that also
completely random networks may have scale-free node distributions gives a new
perspective on the origin of scale-free networks in general.Comment: 5 pages, 3 figure
Azimuthal Anisotropy in High Energy Nuclear Collision - An Approach based on Complex Network Analysis
Recently, a complex network based method of Visibility Graph has been applied
to confirm the scale-freeness and presence of fractal properties in the process
of multiplicity fluctuation. Analysis of data obtained from experiments on
hadron-nucleus and nucleus-nucleus interactions results in values of
Power-of-Scale-freeness-of-Visibility-Graph-(PSVG) parameter extracted from the
visibility graphs. Here, the relativistic nucleus-nucleus interaction data have
been analysed to detect azimuthal-anisotropy by extending the Visibility Graph
method and extracting the average clustering coefficient, one of the important
topological parameters, from the graph. Azimuthal-distributions corresponding
to different pseudorapidity-regions around the central-pseudorapidity value are
analysed utilising the parameter. Here we attempt to correlate the conventional
physical significance of this coefficient with respect to complex-network
systems, with some basic notions of particle production phenomenology, like
clustering and correlation. Earlier methods for detecting anisotropy in
azimuthal distribution, were mostly based on the analysis of statistical
fluctuation. In this work, we have attempted to find deterministic information
on the anisotropy in azimuthal distribution by means of precise determination
of topological parameter from a complex network perspective
Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation
The origin of scale-free degree distributions in the context of networks is
addressed through an analogous non-network model in which the node degree
corresponds to the number of balls in a box and the rewiring of links to balls
moving between the boxes. A statistical mechanical formulation is presented and
the corresponding Hamiltonian is derived. The energy, the entropy, as well as
the degree distribution and its fluctuations are investigated at various
temperatures. The scale-free distribution is shown to correspond to the
degenerate ground state, which has small fluctuations in the degree
distribution and yet a large entropy. We suggest an implication of our results
from the viewpoint of the stability in evolution of networks.Comment: 7 pages, 3 figures. To appear in Europhysics lette
Models and average properties of scale-free directed networks
We extend the merging model for undirected networks by Kim et al. [Eur. Phys.
J. B 43, 369 (2004)] to directed networks and investigate the emerging
scale-free networks. Two versions of the directed merging model, friendly and
hostile merging, give rise to two distinct network types. We uncover that some
non-trivial features of these two network types resemble two levels of a
certain randomization/non-specificity in the link reshuffling during network
evolution. Furthermore the same features show up, respectively, in metabolic
networks and transcriptional networks. We introduce measures that single out
the distinguishing features between the two prototype networks, as well as
point out features which are beyond the prototypes.Comment: 7 pages, 8 figure
Increased signaling entropy in cancer requires the scale-free property of protein interaction networks
One of the key characteristics of cancer cells is an increased phenotypic
plasticity, driven by underlying genetic and epigenetic perturbations. However,
at a systems-level it is unclear how these perturbations give rise to the
observed increased plasticity. Elucidating such systems-level principles is key
for an improved understanding of cancer. Recently, it has been shown that
signaling entropy, an overall measure of signaling pathway promiscuity, and
computable from integrating a sample's gene expression profile with a protein
interaction network, correlates with phenotypic plasticity and is increased in
cancer compared to normal tissue. Here we develop a computational framework for
studying the effects of network perturbations on signaling entropy. We
demonstrate that the increased signaling entropy of cancer is driven by two
factors: (i) the scale-free (or near scale-free) topology of the interaction
network, and (ii) a subtle positive correlation between differential gene
expression and node connectivity. Indeed, we show that if protein interaction
networks were random graphs, described by Poisson degree distributions, that
cancer would generally not exhibit an increased signaling entropy. In summary,
this work exposes a deep connection between cancer, signaling entropy and
interaction network topology.Comment: 20 pages, 5 figures. In Press in Sci Rep 201
Scale-Free Networks beyond Power-Law Degree Distribution
Complex networks across various fields are often considered to be scale free
-- a statistical property usually solely characterized by a power-law
distribution of the nodes' degree . However, this characterization is
incomplete. In real-world networks, the distribution of the degree-degree
distance , a simple link-based metric of network connectivity similar to
, appears to exhibit a stronger power-law distribution than . While
offering an alternative characterization of scale-freeness, the discovery of
raises a fundamental question: do the power laws of and
represent the same scale-freeness? To address this question, here we
investigate the exact asymptotic {relationship} between the distributions of
and , proving that every network with a power-law distribution of
also has a power-law distribution of , but \emph{not} vice versa. This
prompts us to introduce two network models as counterexamples that have a
power-law distribution of but not , constructed using the
preferential attachment and fitness mechanisms, respectively. Both models show
promising accuracy by fitting only one model parameter each when modeling
real-world networks. Our findings suggest that is a more suitable
indicator of scale-freeness and can provide a deeper understanding of the
universality and underlying mechanisms of scale-free networks
All scale-free networks are sparse
We study the realizability of scale free-networks with a given degree
sequence, showing that the fraction of realizable sequences undergoes two
first-order transitions at the values 0 and 2 of the power-law exponent. We
substantiate this finding by analytical reasoning and by a numerical method,
proposed here, based on extreme value arguments, which can be applied to any
given degree distribution. Our results reveal a fundamental reason why large
scale-free networks without constraints on minimum and maximum degree must be
sparse.Comment: 4 pages, 2 figure
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