1,586 research outputs found
Giant strongly connected component of directed networks
We describe how to calculate the sizes of all giant connected components of a
directed graph, including the {\em strongly} connected one. Just to the class
of directed networks, in particular, belongs the World Wide Web. The results
are obtained for graphs with statistically uncorrelated vertices and an
arbitrary joint in,out-degree distribution . We show that if
does not factorize, the relative size of the giant strongly
connected component deviates from the product of the relative sizes of the
giant in- and out-components. The calculations of the relative sizes of all the
giant components are demonstrated using the simplest examples. We explain that
the giant strongly connected component may be less resilient to random damage
than the giant weakly connected one.Comment: 4 pages revtex, 4 figure
Synchronization in Scale Free networks: The role of finite size effects
Synchronization problems in complex networks are very often studied by
researchers due to its many applications to various fields such as
neurobiology, e-commerce and completion of tasks. In particular, Scale Free
networks with degree distribution , are widely used in
research since they are ubiquitous in nature and other real systems. In this
paper we focus on the surface relaxation growth model in Scale Free networks
with , and study the scaling behavior of the fluctuations, in
the steady state, with the system size . We find a novel behavior of the
fluctuations characterized by a crossover between two regimes at a value of
that depends on : a logarithmic regime, found in previous
research, and a constant regime. We propose a function that describes this
crossover, which is in very good agreement with the simulations. We also find
that, for a system size above , the fluctuations decrease with
, which means that the synchronization of the system improves as
increases. We explain this crossover analyzing the role of the
network's heterogeneity produced by the system size and the exponent of the
degree distribution.Comment: 9 pages and 5 figures. Accepted in Europhysics Letter
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
Book Reviews
Book reviews by Edward F. Barrett, Alfred L. Scanlan, Robert T. Molloy, Aaron I. Abell, and Robert E. Sullivan
Diluted antiferromagnet in a ferromagnetic enviroment
The question of robustness of a network under random ``attacks'' is treated
in the framework of critical phenomena. The persistence of spontaneous
magnetization of a ferromagnetic system to the random inclusion of
antiferromagnetic interactions is investigated. After examing the static
properties of the quenched version (in respect to the random antiferromagnetic
interactions) of the model, the persistence of the magnetization is analysed
also in the annealed approximation, and the difference in the results are
discussed
Vertex similarity in networks
We consider methods for quantifying the similarity of vertices in networks.
We propose a measure of similarity based on the concept that two vertices are
similar if their immediate neighbors in the network are themselves similar.
This leads to a self-consistent matrix formulation of similarity that can be
evaluated iteratively using only a knowledge of the adjacency matrix of the
network. We test our similarity measure on computer-generated networks for
which the expected results are known, and on a number of real-world networks
Network synchronization: Optimal and Pessimal Scale-Free Topologies
By employing a recently introduced optimization algorithm we explicitely
design optimally synchronizable (unweighted) networks for any given scale-free
degree distribution. We explore how the optimization process affects
degree-degree correlations and observe a generic tendency towards
disassortativity. Still, we show that there is not a one-to-one correspondence
between synchronizability and disassortativity. On the other hand, we study the
nature of optimally un-synchronizable networks, that is, networks whose
topology minimizes the range of stability of the synchronous state. The
resulting ``pessimal networks'' turn out to have a highly assortative
string-like structure. We also derive a rigorous lower bound for the Laplacian
eigenvalue ratio controlling synchronizability, which helps understanding the
impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex
Networks 2007
Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks
We study numerically the mean access times for random walks on hybrid
disordered structures formed by embedding scale-free networks into regular
lattices, considering different transition rates for steps across lattice bonds
() and across network shortcuts (). For fast shortcuts () and
low shortcut densities, traversal time data collapse onto an universal curve,
while a crossover behavior that can be related to the percolation threshold of
the scale-free network component is identified at higher shortcut densities, in
analogy to similar observations reported recently in Newman-Watts small-world
networks. Furthermore, we observe that random walk traversal times are larger
for networks with a higher degree of inhomogeneity in their shortcut
distribution, and we discuss access time distributions as functions of the
initial and final node degrees. These findings are relevant, in particular,
when considering the optimization of existing information networks by the
addition of a small number of fast shortcut connections.Comment: 8 pages, 6 figures; expanded discussions, added figures and
references. To appear in J Stat Phy
Replication and exploratory analysis of 24 candidate risk polymorphisms for neural tube defects.
BackgroundNeural tube defects (NTDs), which are among the most common congenital malformations, are influenced by environmental and genetic factors. Low maternal folate is the strongest known contributing factor, making variants in genes in the folate metabolic pathway attractive candidates for NTD risk. Multiple studies have identified nominally significant allelic associations with NTDs. We tested whether associations detected in a large Irish cohort could be replicated in an independent population.MethodsReplication tests of 24 nominally significant NTD associations were performed in racially/ethnically matched populations. Family-based tests of fifteen nominally significant single nucleotide polymorphisms (SNPs) were repeated in a cohort of NTD trios (530 cases and their parents) from the United Kingdom, and case-control tests of nine nominally significant SNPs were repeated in a cohort (190 cases, 941 controls) from New York State (NYS). Secondary hypotheses involved evaluating the latter set of nine SNPs for NTD association using alternate case-control models and NTD groupings in white, African American and Hispanic cohorts from NYS.ResultsOf the 24 SNPs tested for replication, ADA rs452159 and MTR rs10925260 were significantly associated with isolated NTDs. Of the secondary tests performed, ARID1A rs11247593 was associated with NTDs in whites, and ALDH1A2 rs7169289 was associated with isolated NTDs in African Americans.ConclusionsWe report a number of associations between SNP genotypes and neural tube defects. These associations were nominally significant before correction for multiple hypothesis testing. These corrections are highly conservative for association studies of untested hypotheses, and may be too conservative for replication studies. We therefore believe the true effect of these four nominally significant SNPs on NTD risk will be more definitively determined by further study in other populations, and eventual meta-analysis
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