83 research outputs found
Clustering properties of a generalised critical Euclidean network
Many real-world networks exhibit scale-free feature, have a small diameter
and a high clustering tendency. We have studied the properties of a growing
network, which has all these features, in which an incoming node is connected
to its th predecessor of degree with a link of length using a
probability proportional to . For , the
network is scale free at with the degree distribution and as in the Barab\'asi-Albert model (). We find a phase boundary in the plane along which
the network is scale-free. Interestingly, we find scale-free behaviour even for
for where the existence of a new universality class
is indicated from the behaviour of the degree distribution and the clustering
coefficients. The network has a small diameter in the entire scale-free region.
The clustering coefficients emulate the behaviour of most real networks for
increasing negative values of on the phase boundary.Comment: 4 pages REVTEX, 4 figure
Growing Scale-Free Networks with Small World Behavior
In the context of growing networks, we introduce a simple dynamical model
that unifies the generic features of real networks: scale-free distribution of
degree and the small world effect. While the average shortest path length
increases logartihmically as in random networks, the clustering coefficient
assumes a large value independent of system size. We derive expressions for the
clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and
highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure
Mean-field theory for clustering coefficients in Barabasi-Albert networks
We applied a mean field approach to study clustering coefficients in
Barabasi-Albert networks. We found that the local clustering in BA networks
depends on the node degree. Analytic results have been compared to extensive
numerical simulations finding a very good agreement for nodes with low degrees.
Clustering coefficient of a whole network calculated from our approach
perfectly fits numerical data.Comment: 8 pages, 3 figure
Nonequilibrium transitions in complex networks: a model of social interaction
We analyze the non-equilibrium order-disorder transition of Axelrod's model
of social interaction in several complex networks. In a small world network, we
find a transition between an ordered homogeneous state and a disordered state.
The transition point is shifted by the degree of spatial disorder of the
underlying network, the network disorder favoring ordered configurations. In
random scale-free networks the transition is only observed for finite size
systems, showing system size scaling, while in the thermodynamic limit only
ordered configurations are always obtained. Thus in the thermodynamic limit the
transition disappears. However, in structured scale-free networks, the phase
transition between an ordered and a disordered phase is restored.Comment: 7 pages revtex4, 10 figures, related material at
http://www.imedea.uib.es/PhysDept/Nonlinear/research_topics/Social
Emergence of influential spreaders in modified rumor models
The burst in the use of online social networks over the last decade has
provided evidence that current rumor spreading models miss some fundamental
ingredients in order to reproduce how information is disseminated. In
particular, recent literature has revealed that these models fail to reproduce
the fact that some nodes in a network have an influential role when it comes to
spread a piece of information. In this work, we introduce two mechanisms with
the aim of filling the gap between theoretical and experimental results. The
first model introduces the assumption that spreaders are not always active
whereas the second model considers the possibility that an ignorant is not
interested in spreading the rumor. In both cases, results from numerical
simulations show a higher adhesion to real data than classical rumor spreading
models. Our results shed some light on the mechanisms underlying the spreading
of information and ideas in large social systems and pave the way for more
realistic diffusion models.Comment: 14 Pages, 6 figures, accepted for publication in Journal of
Statistical Physic
Live and Dead Nodes
In this paper, we explore the consequences of a distinction between `live'
and `dead' network nodes; `live' nodes are able to acquire new links whereas
`dead' nodes are static. We develop an analytically soluble growing network
model incorporating this distinction and show that it can provide a
quantitative description of the empirical network composed of citations and
references (in- and out-links) between papers (nodes) in the SPIRES database of
scientific papers in high energy physics. We also demonstrate that the death
mechanism alone can result in power law degree distributions for the resulting
network.Comment: 12 pages, 3 figures. To be published in Computational and
Mathematical Organization Theor
The effect of aging on network structure
In network evolution, the effect of aging is universal: in scientific
collaboration network, scientists have a finite time span of being active; in
movie actors network, once popular stars are retiring from stage; devices on
the Internet may become outmoded with techniques developing so rapidly. Here we
find in citation networks that this effect can be represented by an exponential
decay factor, , where is the node age, while other
evolving networks (the Internet for instance) may have different types of
aging, for example, a power-law decay factor, which is also studied and
compared. It has been found that as soon as such a factor is introduced to the
Barabasi-Albert Scale-Free model, the network will be significantly
transformed. The network will be clustered even with infinitely large size, and
the clustering coefficient varies greatly with the intensity of the aging
effect, i.e. it increases linearly with for small values of
and decays exponentially for large values of . At the same time, the
aging effect may also result in a hierarchical structure and a disassortative
degree-degree correlation. Generally the aging effect will increase the average
distance between nodes, but the result depends on the type of the decay factor.
The network appears like a one-dimensional chain when exponential decay is
chosen, but with power-law decay, a transformation process is observed, i.e.,
from a small-world network to a hypercubic lattice, and to a one-dimensional
chain finally. The disparities observed for different choices of the decay
factor, in clustering, average node distance and probably other aspects not yet
identified, are believed to bear significant meaning on empirical data
acquisition.Comment: 8 pages, 9 figures,V2, accepted for publication in Phys. Rev.
Gaussian Tunneling Model of c-Axis Twist Josephson Junctions
We calculate the critical current density for c-axis Josephson
tunneling between identical high temperature superconductors twisted an angle
about the c-axis. We model the tunneling matrix element squared as a
Gaussian in the change of wavevector q parallel to the junction, . The
obtained for the s- and extended-s-wave order parameters (OP's) are consistent
with the BiSrCaCuO data of Li {\it et al.}, but only
for strongly incoherent tunneling, . A -wave OP
is always inconsistent with the data. In addition, we show that the apparent
conventional sum rule violation observed by Basov et al. might be
understandable in terms of incoherent c-axis tunneling, provided that the OP is
not -wave.Comment: 6 pages, 6 figure
Solution of voter model dynamics on annealed small-world networks
An analytical study of the behavior of the voter model on the small-world
topology is performed. In order to solve the equations for the dynamics, we
consider an annealed version of the Watts-Strogatz (WS) network, where
long-range connections are randomly chosen at each time step. The resulting
dynamics is as rich as on the original WS network. A temporal scale
separates a quasi-stationary disordered state with coexisting domains from a
fully ordered frozen configuration. is proportional to the number of
nodes in the network, so that the system remains asymptotically disordered in
the thermodynamic limit.Comment: 11 pages, 4 figures, published version. Added section with extension
to generic number of nearest neighbor
Properties of highly clustered networks
We propose and solve exactly a model of a network that has both a tunable
degree distribution and a tunable clustering coefficient. Among other things,
our results indicate that increased clustering leads to a decrease in the size
of the giant component of the network. We also study SIR-type epidemic
processes within the model and find that clustering decreases the size of
epidemics, but also decreases the epidemic threshold, making it easier for
diseases to spread. In addition, clustering causes epidemics to saturate
sooner, meaning that they infect a near-maximal fraction of the network for
quite low transmission rates.Comment: 7 pages, 2 figures, 1 tabl
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