74 research outputs found
Connectivity strategies to enhance the capacity of weight-bearing networks
The connectivity properties of a weight-bearing network are exploited to
enhance it's capacity. We study a 2-d network of sites where the weight-bearing
capacity of a given site depends on the capacities of the sites connected to it
in the layers above. The network consists of clusters viz. a set of sites
connected with each other with the largest such collection of sites being
denoted as the maximal cluster. New connections are made between sites in
successive layers using two distinct strategies. The key element of our
strategies consists of adding as many disjoint clusters as possible to the
sites on the trunk of the maximal cluster. The new networks can bear much
higher weights than the original networks and have much lower failure rates.
The first strategy leads to a greater enhancement of stability whereas the
second leads to a greater enhancement of capacity compared to the original
networks. The original network used here is a typical example of the branching
hierarchical class. However the application of strategies similar to ours can
yield useful results in other types of networks as well.Comment: 17 pages, 3 EPS files, 5 PS files, Phys. Rev. E (to appear
Evolution of community structure in the world trade web
In this note we study the bilateral merchandise trade flows between 186
countries over the 1948-2005 period using data from the International Monetary
Fund. We use Pajek to identify network structure and behavior across thresholds
and over time. In particular, we focus on the evolution of trade "islands" in
the a world trade network in which countries are linked with directed edges
weighted according to fraction of total dollars sent from one country to
another. We find mixed evidence for globalization.Comment: To be submitted to APFA 6 Proceedings, 8 pages, 3 Figure
Large-scale structural organization of social networks
The characterization of large-scale structural organization of social
networks is an important interdisciplinary problem. We show, by using scaling
analysis and numerical computation, that the following factors are relevant for
models of social networks: the correlation between friendship ties among people
and the position of their social groups, as well as the correlation between the
positions of different social groups to which a person belongs.Comment: 5 pages, 3 figures, Revte
Interface Motion and Pinning in Small World Networks
We show that the nonequilibrium dynamics of systems with many interacting
elements located on a small-world network can be much slower than on regular
networks. As an example, we study the phase ordering dynamics of the Ising
model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at
zero temperature. In one and two dimensions, small-world features produce
dynamically frozen configurations, disordered at large length scales, analogous
of random field models. This picture differs from the common knowledge
(supported by equilibrium results) that ferromagnetic short-cuts connections
favor order and uniformity. We briefly discuss some implications of these
results regarding the dynamics of social changes.Comment: 4 pages, 5 figures with minor corrections. To appear in Phys. Rev.
A model for cascading failures in complex networks
Large but rare cascades triggered by small initial shocks are present in most
of the infrastructure networks. Here we present a simple model for cascading
failures based on the dynamical redistribution of the flow on the network. We
show that the breakdown of a single node is sufficient to collapse the
efficiency of the entire system if the node is among the ones with largest
load. This is particularly important for real-world networks with an highly
hetereogeneous distribution of loads as the Internet and electrical power
grids.Comment: 4 pages, 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
A motif-based approach to network epidemics
Networks have become an indispensable tool in modelling infectious diseases, with the structure of epidemiologically relevant contacts known to affect both the dynamics of the infection process and the efficacy of intervention strategies. One of the key reasons for this is the presence of clustering in contact networks, which is typically analysed in terms of prevalence of triangles in the network. We present a more general approach, based on the prevalence of different four-motifs, in the context of ODE approximations to network dynamics. This is shown to outperform existing models for a range of small world networks
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
Networks of noisy oscillators with correlated degree and frequency dispersion
We investigate how correlations between the diversity of the connectivity of
networks and the dynamics at their nodes affect the macroscopic behavior. In
particular, we study the synchronization transition of coupled stochastic phase
oscillators that represent the node dynamics. Crucially in our work, the
variability in the number of connections of the nodes is correlated with the
width of the frequency distribution of the oscillators. By numerical
simulations on Erd\"os-R\'enyi networks, where the frequencies of the
oscillators are Gaussian distributed, we make the counterintuitive observation
that an increase in the strength of the correlation is accompanied by an
increase in the critical coupling strength for the onset of synchronization. We
further observe that the critical coupling can solely depend on the average
number of connections or even completely lose its dependence on the network
connectivity. Only beyond this state, a weighted mean-field approximation
breaks down. If noise is present, the correlations have to be stronger to yield
similar observations.Comment: 6 pages, 2 figure
Topology of the conceptual network of language
We define two words in a language to be connected if they express similar
concepts. The network of connections among the many thousands of words that
make up a language is important not only for the study of the structure and
evolution of languages, but also for cognitive science. We study this issue
quantitatively, by mapping out the conceptual network of the English language,
with the connections being defined by the entries in a Thesaurus dictionary. We
find that this network presents a small-world structure, with an amazingly
small average shortest path, and appears to exhibit an asymptotic scale-free
feature with algebraic connectivity distribution.Comment: 4 pages, 2 figures, Revte
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