1,464,988 research outputs found
Spectral analysis of deformed random networks
We study spectral behavior of sparsely connected random networks under the
random matrix framework. Sub-networks without any connection among them form a
network having perfect community structure. As connections among the
sub-networks are introduced, the spacing distribution shows a transition from
the Poisson statistics to the Gaussian orthogonal ensemble statistics of random
matrix theory. The eigenvalue density distribution shows a transition to the
Wigner's semicircular behavior for a completely deformed network. The range for
which spectral rigidity, measured by the Dyson-Mehta statistics,
follows the Gaussian orthogonal ensemble statistics depends upon the
deformation of the network from the perfect community structure. The spacing
distribution is particularly useful to track very slight deformations of the
network from a perfect community structure, whereas the density distribution
and the statistics remain identical to the undeformed network. On
the other hand the statistics is useful for the larger deformation
strengths. Finally, we analyze the spectrum of a protein-protein interaction
network for Helicobacter, and compare the spectral behavior with those of the
model networks.Comment: accepted for publication in Phys. Rev. E (replaced with the final
version
Dynamic Computation of Network Statistics via Updating Schema
In this paper we derive an updating scheme for calculating some important
network statistics such as degree, clustering coefficient, etc., aiming at
reduce the amount of computation needed to track the evolving behavior of large
networks; and more importantly, to provide efficient methods for potential use
of modeling the evolution of networks. Using the updating scheme, the network
statistics can be computed and updated easily and much faster than
re-calculating each time for large evolving networks. The update formula can
also be used to determine which edge/node will lead to the extremal change of
network statistics, providing a way of predicting or designing evolution rule
of networks.Comment: 17 pages, 6 figure
Failed "nonaccelerating" models of prokaryote gene regulatory networks
Much current network analysis is predicated on the assumption that important
biological networks will either possess scale free or exponential statistics
which are independent of network size allowing unconstrained network growth
over time. In this paper, we demonstrate that such network growth models are
unable to explain recent comparative genomics results on the growth of
prokaryote regulatory gene networks as a function of gene number. This failure
largely results as prokaryote regulatory gene networks are "accelerating" and
have total link numbers growing faster than linearly with network size and so
can exhibit transitions from stationary to nonstationary statistics and from
random to scale-free to regular statistics at particular critical network
sizes. In the limit, these networks can undergo transitions so marked as to
constrain network sizes to be below some critical value. This is of interest as
the regulatory gene networks of single celled prokaryotes are indeed
characterized by an accelerating quadratic growth with gene count and are size
constrained to be less than about 10,000 genes encoded in DNA sequence of less
than about 10 megabases. We develop two "nonaccelerating" network models of
prokaryote regulatory gene networks in an endeavor to match observation and
demonstrate that these approaches fail to reproduce observed statistics.Comment: Corrected error in biological input parameter: 13 pages, 9 figure
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