2,330 research outputs found
Scaling of critical connectivity of mobile ad hoc communication networks
In this paper, critical global connectivity of mobile ad hoc communication
networks (MAHCN) is investigated. We model the two-dimensional plane on which
nodes move randomly with a triangular lattice. Demanding the best communication
of the network, we account the global connectivity as a function of
occupancy of sites in the lattice by mobile nodes. Critical phenomena
of the connectivity for different transmission ranges are revealed by
numerical simulations, and these results fit well to the analysis based on the
assumption of homogeneous mixing . Scaling behavior of the connectivity is
found as , where , is
the length unit of the triangular lattice and is the scaling index in
the universal function . The model serves as a sort of site percolation
on dynamic complex networks relative to geometric distance. Moreover, near each
critical corresponding to certain transmission range , there
exists a cut-off degree below which the clustering coefficient of such
self-organized networks keeps a constant while the averaged nearest neighbor
degree exhibits a unique linear variation with the degree k, which may be
useful to the designation of real MAHCN.Comment: 6 pages, 6 figure
Transport on river networks: A dynamical approach
This study is motivated by problems related to environmental transport on
river networks. We establish statistical properties of a flow along a directed
branching network and suggest its compact parameterization. The downstream
network transport is treated as a particular case of nearest-neighbor
hierarchical aggregation with respect to the metric induced by the branching
structure of the river network. We describe the static geometric structure of a
drainage network by a tree, referred to as the static tree, and introduce an
associated dynamic tree that describes the transport along the static tree. It
is well known that the static branching structure of river networks can be
described by self-similar trees (SSTs); we demonstrate that the corresponding
dynamic trees are also self-similar. We report an unexpected phase transition
in the dynamics of three river networks, one from California and two from
Italy, demonstrate the universal features of this transition, and seek to
interpret it in hydrological terms.Comment: 38 pages, 15 figure
Dynamical real-space renormalization group calculations with a new clustering scheme on random networks
We have defined a new type of clustering scheme preserving the connectivity
of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving
process. Our new clustering scheme performs much better for correlation length
and dynamical critical exponents in high dimensions, where the conventional
Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we
find the dynamical critical exponents for the kinetic Ising Model to be z=2.13
and z=2.09, respectively at pure Ising fixed point. These values are in very
good agreement with recent Monte Carlo results. We investigate the phase
diagram and the critical behaviour for randomly bond diluted lattices in d=2
and 3, in the light of this new transformation. We also provide exact
correlation exponent and dynamical critical exponent values on hierarchical
lattices with power-law degree distributions, both in the pure and random
cases.Comment: 8 figure
Topology and correlations in structured scale-free networks
We study a recently introduced class of scale-free networks showing a high
clustering coefficient and non-trivial connectivity correlations. We find that
the connectivity probability distribution strongly depends on the fine details
of the model. We solve exactly the case of low average connectivity, providing
also exact expressions for the clustering and degree correlation functions. The
model also exhibits a lack of small world properties in the whole parameters
range. We discuss the physical properties of these networks in the light of the
present detailed analysis.Comment: 10 pages, 9 figure
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
Optimal construction of k-nearest neighbor graphs for identifying noisy clusters
We study clustering algorithms based on neighborhood graphs on a random
sample of data points. The question we ask is how such a graph should be
constructed in order to obtain optimal clustering results. Which type of
neighborhood graph should one choose, mutual k-nearest neighbor or symmetric
k-nearest neighbor? What is the optimal parameter k? In our setting, clusters
are defined as connected components of the t-level set of the underlying
probability distribution. Clusters are said to be identified in the
neighborhood graph if connected components in the graph correspond to the true
underlying clusters. Using techniques from random geometric graph theory, we
prove bounds on the probability that clusters are identified successfully, both
in a noise-free and in a noisy setting. Those bounds lead to several
conclusions. First, k has to be chosen surprisingly high (rather of the order n
than of the order log n) to maximize the probability of cluster identification.
Secondly, the major difference between the mutual and the symmetric k-nearest
neighbor graph occurs when one attempts to detect the most significant cluster
only.Comment: 31 pages, 2 figure
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