13,606 research outputs found
Scale-free networks with tunable degree distribution exponents
We propose and study a model of scale-free growing networks that gives a
degree distribution dominated by a power-law behavior with a model-dependent,
hence tunable, exponent. The model represents a hybrid of the growing networks
based on popularity-driven and fitness-driven preferential attachments. As the
network grows, a newly added node establishes new links to existing nodes
with a probability based on popularity of the existing nodes and a
probability based on fitness of the existing nodes. An explicit form of
the degree distribution is derived within a mean field approach. For
reasonably large , , where the
function is dominated by the behavior of for small
values of and becomes -independent as , and is a
model-dependent exponent. The degree distribution and the exponent
are found to be in good agreement with results obtained by extensive numerical
simulations.Comment: 12 pages, 2 figures, submitted to PR
Analysis of Nonlinear Synchronization Dynamics of Oscillator Networks by Laplacian Spectral Methods
We analyze the synchronization dynamics of phase oscillators far from the
synchronization manifold, including the onset of synchronization on scale-free
networks with low and high clustering coefficients. We use normal coordinates
and corresponding time-averaged velocities derived from the Laplacian matrix,
which reflects the network's topology. In terms of these coordinates,
synchronization manifests itself as a contraction of the dynamics onto
progressively lower-dimensional submanifolds of phase space spanned by
Laplacian eigenvectors with lower eigenvalues. Differences between high and low
clustering networks can be correlated with features of the Laplacian spectrum.
For example, the inhibition of full synchoronization at high clustering is
associated with a group of low-lying modes that fail to lock even at strong
coupling, while the advanced partial synchronizationat low coupling noted
elsewhere is associated with high-eigenvalue modes.Comment: Revised version: References added, introduction rewritten, additional
minor changes for clarit
Phase transition in the modified fiber bundle model
We extend the standard fiber bundle model (FBM) with the local load sharing
in such a way that the conservation of the total load is relaxed when an
isolated fiber is broken. In this modified FBM in one dimension (1D), it is
revealed that the model exhibits a well-defined phase transition at a finite
nonzero value of the load, which is in contrast to the standard 1D FBM. The
modified FBM defined in the Watts-Strogatz network is also investigated, and
found is the existences of two distinct transitions: one discontinuous and the
other continuous. The effects of the long-range shortcuts are also discussed.Comment: 7 pages, to appear in Europhys. Let
Instability of scale-free networks under node-breaking avalanches
The instability introduced in a large scale-free network by the triggering of
node-breaking avalanches is analyzed using the fiber-bundle model as conceptual
framework. We found, by measuring the size of the giant component, the
avalanche size distribution and other quantities, the existence of an abrupt
transition. This test of strength for complex networks like Internet is more
stringent than others recently considered like the random removal of nodes,
analyzed within the framework of percolation theory. Finally, we discuss the
possible implications of our results and their relevance in forecasting
cascading failures in scale-free networks.Comment: 4 pages, 4 figures, final version to be published in Europhys. Let
Monte Carlo simulation of the transmission of measles: Beyond the mass action principle
We present a Monte Carlo simulation of the transmission of measles within a
population sample during its growing and equilibrium states by introducing two
different vaccination schedules of one and two doses. We study the effects of
the contact rate per unit time as well as the initial conditions on the
persistence of the disease. We found a weak effect of the initial conditions
while the disease persists when lies in the range 1/L-10/L ( being
the latent period). Further comparison with existing data, prediction of future
epidemics and other estimations of the vaccination efficiency are provided.
Finally, we compare our approach to the models using the mass action
principle in the first and another epidemic region and found the incidence
independent of the number of susceptibles after the epidemic peak while it
strongly fluctuates in its growing region. This method can be easily applied to
other human, animals and vegetable diseases and includes more complicated
parameters.Comment: 15 pages, 4 figures, 1 table, Submitted to Phys.Rev.
Classes of behavior of small-world networks
Small-world networks are the focus of recent interest because they appear to
circumvent many of the limitations of either random networks or regular
lattices as frameworks for the study of interaction networks of complex
systems. Here, we report an empirical study of the statistical properties of a
variety of diverse real-world networks. We present evidence of the occurrence
of three classes of small-world networks: (a) scale-free networks,
characterized by a vertex connectivity distribution that decays as a power law;
(b) broad-scale networks, characterized by a connectivity distribution that has
a power-law regime followed by a sharp cut-off; (c) single-scale networks,
characterized by a connectivity distribution with a fast decaying tail.
Moreover, we note for the classes of broad-scale and single-scale networks that
there are constraints limiting the addition of new links. Our results suggest
that the nature of such constraints may be the controlling factor for the
emergence of different classes of networks
Irreversible growth of binary mixtures on small-world networks
Binary mixtures growing on small-world networks under far-from-equilibrium
conditions are studied by means of extensive Monte Carlo simulations. For any
positive value of the shortcut fraction of the network (), the system
undergoes a continuous order-disorder phase transition, while it is noncritical
in the regular lattice limit (). Using finite-size scaling relations, the
phase diagram is obtained in the thermodynamic limit and the critical exponents
are evaluated. The small-world networks are thus shown to trigger criticality,
a remarkable phenomenon which is analogous to similar observations reported
recently in the investigation of equilibrium systems.Comment: 7 pages, 7 figures; added/removed references and modified
presentation. To appear in PR
Netons: Vibrations of Complex Networks
We consider atoms interacting each other through the topological structure of
a complex network and investigate lattice vibrations of the system, the quanta
of which we call {\em netons} for convenience. The density of neton levels,
obtained numerically, reveals that unlike a local regular lattice, the system
develops a gap of a finite width, manifesting extreme rigidity of the network
structure at low energies. Two different network models, the small-world
network and the scale-free network, are compared: The characteristic structure
of the former is described by an additional peak in the level density whereas a
power-law tail is observed in the latter, indicating excitability of netons at
arbitrarily high energies. The gap width is also found to vanish in the
small-world network when the connection range .Comment: 9 pages, 6 figures, to appear in JP
Weighted Evolving Networks
Many biological, ecological and economic systems are best described by
weighted networks, as the nodes interact with each other with varying strength.
However, most network models studied so far are binary, the link strength being
either 0 or 1. In this paper we introduce and investigate the scaling
properties of a class of models which assign weights to the links as the
network evolves. The combined numerical and analytical approach indicates that
asymptotically the total weight distribution converges to the scaling behavior
of the connectivity distribution, but this convergence is hampered by strong
logarithmic corrections.Comment: 5 pages, 3 figure
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