1,093 research outputs found
Unified model for network dynamics exhibiting nonextensive statistics
We introduce a dynamical network model which unifies a number of network
families which are individually known to exhibit -exponential degree
distributions. The present model dynamics incorporates static (non-growing)
self-organizing networks, preferentially growing networks, and (preferentially)
rewiring networks. Further, it exhibits a natural random graph limit. The
proposed model generalizes network dynamics to rewiring and growth modes which
depend on internal topology as well as on a metric imposed by the space they
are embedded in. In all of the networks emerging from the presented model we
find q-exponential degree distributions over a large parameter space. We
comment on the parameter dependence of the corresponding entropic index q for
the degree distributions, and on the behavior of the clustering coefficients
and neighboring connectivity distributions.Comment: 11 pages 8 fig
Quantifying the connectivity of a network: The network correlation function method
Networks are useful for describing systems of interacting objects, where the
nodes represent the objects and the edges represent the interactions between
them. The applications include chemical and metabolic systems, food webs as
well as social networks. Lately, it was found that many of these networks
display some common topological features, such as high clustering, small
average path length (small world networks) and a power-law degree distribution
(scale free networks). The topological features of a network are commonly
related to the network's functionality. However, the topology alone does not
account for the nature of the interactions in the network and their strength.
Here we introduce a method for evaluating the correlations between pairs of
nodes in the network. These correlations depend both on the topology and on the
functionality of the network. A network with high connectivity displays strong
correlations between its interacting nodes and thus features small-world
functionality. We quantify the correlations between all pairs of nodes in the
network, and express them as matrix elements in the correlation matrix. From
this information one can plot the correlation function for the network and to
extract the correlation length. The connectivity of a network is then defined
as the ratio between this correlation length and the average path length of the
network. Using this method we distinguish between a topological small world and
a functional small world, where the latter is characterized by long range
correlations and high connectivity. Clearly, networks which share the same
topology, may have different connectivities, based on the nature and strength
of their interactions. The method is demonstrated on metabolic networks, but
can be readily generalized to other types of networks.Comment: 10 figure
Inhomogeneous substructures hidden in random networks
We study the structure of the load-based spanning tree (LST) that carries the
maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is
given by the edge-betweenness centrality, the effective number of shortest
paths through the edge. We find that the LSTs present very inhomogeneous
structures in contrast to the homogeneous structures of the original networks.
Moreover, it turns out that the structure of the LST changes dramatically as
the edge density of an ER network increases, from scale free with a cutoff,
scale free, to a starlike topology. These would not be possible if the weights
are randomly distributed, which implies that topology of the shortest path is
correlated in spite of the homogeneous topology of the random network.Comment: 4 pages, 4 figure
Optimization of Robustness of Complex Networks
Networks with a given degree distribution may be very resilient to one type
of failure or attack but not to another. The goal of this work is to determine
network design guidelines which maximize the robustness of networks to both
random failure and intentional attack while keeping the cost of the network
(which we take to be the average number of links per node) constant. We find
optimal parameters for: (i) scale free networks having degree distributions
with a single power-law regime, (ii) networks having degree distributions with
two power-law regimes, and (iii) networks described by degree distributions
containing two peaks. Of these various kinds of distributions we find that the
optimal network design is one in which all but one of the nodes have the same
degree, (close to the average number of links per node), and one node is
of very large degree, , where is the number of nodes in
the network.Comment: Accepted for publication in European Physical Journal
Giant Clusters in Random Ad Hoc Networks
The present paper introduces ad hoc communication networks as examples of
large scale real networks that can be prospected by statistical means. A
description of giant cluster formation based on the single parameter of node
neighbor numbers is given along with the discussion of some asymptotic aspects
of the giant cluster sizes.Comment: 6 pages, 5 figures; typos and correction
Random graph model with power-law distributed triangle subgraphs
Clustering is well-known to play a prominent role in the description and
understanding of complex networks, and a large spectrum of tools and ideas have
been introduced to this end. In particular, it has been recognized that the
abundance of small subgraphs is important. Here, we study the arrangement of
triangles in a model for scale-free random graphs and determine the asymptotic
behavior of the clustering coefficient, the average number of triangles, as
well as the number of triangles attached to the vertex of maximum degree. We
prove that triangles are power-law distributed among vertices and characterized
by both vertex and edge coagulation when the degree exponent satisfies
; furthermore, a finite density of triangles appears as
.Comment: 4 pages, 2 figure; v2: major conceptual change
Robustness of interdependent networks under targeted attack
When an initial failure of nodes occurs in interdependent networks, a cascade
of failure between the networks occurs. Earlier studies focused on random
initial failures. Here we study the robustness of interdependent networks under
targeted attack on high or low degree nodes. We introduce a general technique
and show that the {\it targeted-attack} problem in interdependent networks can
be mapped to the {\it random-attack} problem in a transformed pair of
interdependent networks. We find that when the highly connected nodes are
protected and have lower probability to fail, in contrast to single scale free
(SF) networks where the percolation threshold , coupled SF networks are
significantly more vulnerable with significantly larger than zero. The
result implies that interdependent networks are difficult to defend by
strategies such as protecting the high degree nodes that have been found useful
to significantly improve robustness of single networks.Comment: 11 pages, 2 figure
Microscopic analysis of multipole susceptibility of actinide dioxides: A scenario of multipole ordering in AmO
By evaluating multipole susceptibility of a seven-orbital impurity Anderson
model with the use of a numerical renormalization group method, we discuss
possible multipole states of actinide dioxides at low temperatures. In
particular, here we point out a possible scenario for multipole ordering in
americium dioxide. For Am ion with five electrons, it is considered
that the ground state is doublet and the first excited state is
quartet, but we remark that the ground state is easily
converted due to the competition between spin-orbit coupling and Coulomb
interactions. Then, we find that the quartet can be the ground
state of AmO even for the same crystalline electric field potential. In the
case of quartet ground state, the numerical results suggest that
high-order multipoles such as quadrupole and octupole can be relevant to
AmO.Comment: 8 pages, 4 figures. To appear in Phys. Rev.
Analytical Solution of a Stochastic Content Based Network Model
We define and completely solve a content-based directed network whose nodes
consist of random words and an adjacency rule involving perfect or approximate
matches, for an alphabet with an arbitrary number of letters. The analytic
expression for the out-degree distribution shows a crossover from a leading
power law behavior to a log-periodic regime bounded by a different power law
decay. The leading exponents in the two regions have a weak dependence on the
mean word length, and an even weaker dependence on the alphabet size. The
in-degree distribution, on the other hand, is much narrower and does not show
scaling behavior. The results might be of interest for understanding the
emergence of genomic interaction networks, which rely, to a large extent, on
mechanisms based on sequence matching, and exhibit similar global features to
those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to
gene regulation networks, fixed minor errors and replaced fig. 4. Main body
of paper (model and calculations) remains unchanged. Submitted for
publicatio
Coherence in scale-free networks of chaotic maps
We study fully synchronized states in scale-free networks of chaotic logistic
maps as a function of both dynamical and topological parameters. Three
different network topologies are considered: (i) random scale-free topology,
(ii) deterministic pseudo-fractal scale-free network, and (iii) Apollonian
network. For the random scale-free topology we find a coupling strength
threshold beyond which full synchronization is attained. This threshold scales
as , where is the outgoing connectivity and depends on the
local nonlinearity. For deterministic scale-free networks coherence is observed
only when the coupling strength is proportional to the neighbor connectivity.
We show that the transition to coherence is of first-order and study the role
of the most connected nodes in the collective dynamics of oscillators in
scale-free networks.Comment: 9 pages, 8 figure
- âŠ