4,400 research outputs found
Condensation in a zero range process on weighted scale-free networks
We study the condensation phenomenon in a zero range process on weighted
scale-free networks in order to show how the weighted transport influences the
particle condensation. Instead of the approach of grand canonical ensemble
which is generally used in a zero range process, we introduce an alternate
approach of the mean field equations to study the dynamics of particle
transport. We find that the condensation on scale-free network is easier to
occur in the case of weighted transport than in the case of weight-free. In the
weighted transport, especially, a dynamical condensation is even possible for
the case of no interaction among particles, which is impossible in the case of
weight-free.Comment: 6 pages, 4 figure
Condensation transitions in a model for a directed network with weighted links
An exactly solvable model for the rewiring dynamics of weighted, directed
networks is introduced. Simulations indicate that the model exhibits two types
of condensation: (i) a phase in which, for each node, a finite fraction of its
total out-strength condenses onto a single link; (ii) a phase in which a finite
fraction of the total weight in the system is directed into a single node. A
virtue of the model is that its dynamics can be mapped onto those of a
zero-range process with many species of interacting particles -- an exactly
solvable model of particles hopping between the sites of a lattice. This
mapping, which is described in detail, guides the analysis of the steady state
of the network model and leads to theoretical predictions for the conditions
under which the different types of condensation may be observed. A further
advantage of the mapping is that, by exploiting what is known about exactly
solvable generalisations of the zero-range process, one can infer a number of
generalisations of the network model and dynamics which remain exactly
solvable.Comment: 23 pages, 8 figure
Properties of Random Graphs with Hidden Color
We investigate in some detail a recently suggested general class of ensembles
of sparse undirected random graphs based on a hidden stub-coloring, with or
without the restriction to nondegenerate graphs. The calculability of local and
global structural properties of graphs from the resulting ensembles is
demonstrated. Cluster size statistics are derived with generating function
techniques, yielding a well-defined percolation threshold. Explicit rules are
derived for the enumeration of small subgraphs. Duality and redundancy is
discussed, and subclasses corresponding to commonly studied models are
identified.Comment: 14 pages, LaTeX, no figure
Complex Networks and Symmetry I: A Review
In this review we establish various connections between complex networks and
symmetry. While special types of symmetries (e.g., automorphisms) are studied
in detail within discrete mathematics for particular classes of deterministic
graphs, the analysis of more general symmetries in real complex networks is far
less developed. We argue that real networks, as any entity characterized by
imperfections or errors, necessarily require a stochastic notion of invariance.
We therefore propose a definition of stochastic symmetry based on graph
ensembles and use it to review the main results of network theory from an
unusual perspective. The results discussed here and in a companion paper show
that stochastic symmetry highlights the most informative topological properties
of real networks, even in noisy situations unaccessible to exact techniques.Comment: Final accepted versio
Causal and homogeneous networks
Growing networks have a causal structure. We show that the causality strongly
influences the scaling and geometrical properties of the network. In particular
the average distance between nodes is smaller for causal networks than for
corresponding homogeneous networks. We explain the origin of this effect and
illustrate it using as an example a solvable model of random trees. We also
discuss the issue of stability of the scale-free node degree distribution. We
show that a surplus of links may lead to the emergence of a singular node with
the degree proportional to the total number of links. This effect is closely
related to the backgammon condensation known from the balls-in-boxes model.Comment: short review submitted to AIP proceedings, CNET2004 conference;
changes in the discussion of the distance distribution for growing trees,
Fig. 6-right change
Ensemble equivalence for distinguishable particles
Statistics of distinguishable particles has become relevant in systems of
colloidal particles and in the context of applications of statistical mechanics
to complex networks. When studying these type of systems with the standard
textbook formalism, non-physical results such as non-extensive entropies are
obtained. In this paper, we will show that the commonly used expression for the
partition function of a system of distinguishable particles leads to huge
fluctuations of the number of particles in the grand canonical ensemble and,
consequently, to non-equivalence of statistical ensembles. We will see how a
new proposed definition for the entropy of distinguishable particles by
Swendsen [J. Stat. Phys. 107, 1143 (2002)] solves the problem and restores
ensemble equivalence. We also show that the new proposal for the partition
function does not produce any inconsistency for a system of distinguishable
localized particles, where the monoparticular partition function is not
extensive
Centrality anomalies in complex networks as a result of model over-simplification
Tremendous advances have been made in our understanding of the properties and
evolution of complex networks. These advances were initially driven by
information-poor empirical networks and theoretical analysis of unweighted and
undirected graphs. Recently, information-rich empirical data complex networks
supported the development of more sophisticated models that include edge
directionality and weight properties, and multiple layers. Many studies still
focus on unweighted undirected description of networks, prompting an essential
question: how to identify when a model is simpler than it must be? Here, we
argue that the presence of centrality anomalies in complex networks is a result
of model over-simplification. Specifically, we investigate the well-known
anomaly in betweenness centrality for transportation networks, according to
which highly connected nodes are not necessarily the most central. Using a
broad class of network models with weights and spatial constraints and four
large data sets of transportation networks, we show that the unweighted
projection of the structure of these networks can exhibit a significant
fraction of anomalous nodes compared to a random null model. However, the
weighted projection of these networks, compared with an appropriated null
model, significantly reduces the fraction of anomalies observed, suggesting
that centrality anomalies are a symptom of model over-simplification. Because
lack of information-rich data is a common challenge when dealing with complex
networks and can cause anomalies that misestimate the role of nodes in the
system, we argue that sufficiently sophisticated models be used when anomalies
are detected.Comment: 14 pages, including 9 figures. APS style. Accepted for publication in
New Journal of Physic
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