60 research outputs found
Optimal network topologies for local search with congestion
The problem of searchability in decentralized complex networks is of great
importance in computer science, economy and sociology. We present a formalism
that is able to cope simultaneously with the problem of search and the
congestion effects that arise when parallel searches are performed, and obtain
expressions for the average search cost--written in terms of the search
algorithm and the topological properties of the network--both in presence and
abscence of congestion. This formalism is used to obtain optimal network
structures for a system using a local search algorithm. It is found that only
two classes of networks can be optimal: star-like configurations, when the
number of parallel searches is small, and homogeneous-isotropic configurations,
when the number of parallel searches is large.Comment: 4 pages. Final version accepted in PR
Optimization in Networks
The recent surge in the network modeling of complex systems has set the stage
for a new era in the study of fundamental and applied aspects of optimization
in collective behavior. This Focus Issue presents an extended view of the state
of the art in this field and includes articles from a large variety of domains
where optimization manifests itself, including physical, biological, social,
and technological networked systems.Comment: Opening article of the CHAOS Focus Issue "Optimization in Networks",
available at http://link.aip.org/link/?CHA/17/2/htmlto
Rare events statistics of random walks on networks: localization and other dynamical phase transitions
Rare event statistics for random walks on complex networks are investigated
using the large deviations formalism. Within this formalism, rare events are
realized as typical events in a suitably deformed path-ensemble, and their
statistics can be studied in terms of spectral properties of a deformed Markov
transition matrix. We observe two different types of phase transition in such
systems: (i) rare events which are singled out for sufficiently large values of
the deformation parameter may correspond to {\em localized\/} modes of the
deformed transition matrix, (ii) "mode-switching transitions" may occur as the
deformation parameter is varied. Details depend on the nature of the observable
for which the rare event statistics is studied, as well as on the underlying
graph ensemble. In the present letter we report on the statistics of the
average degree of the nodes visited along a random walk trajectory in
Erd\H{o}s-R\'enyi networks. Large deviations rate functions and localization
properties are studied numerically. For observables of the type considered
here, we also derive an analytical approximation for the Legendre transform of
the large-deviations rate function, which is valid in the large connectivity
limit. It is found to agree well with simulations.Comment: 5 pages, 3 figure
Information transfer in community structured multiplex networks
The study of complex networks that account for different types of
interactions has become a subject of interest in the last few years, specially
because its representational power in the description of users interactions in
diverse online social platforms (Facebook, Twitter, Instagram, etc.). The
mathematical description of these interacting networks has been coined under
the name of multilayer networks, where each layer accounts for a type of
interaction. It has been shown that diffusive processes on top of these
networks present a phenomenology that cannot be explained by the naive
superposition of single layer diffusive phenomena but require the whole
structure of interconnected layers. Nevertheless, the description of diffusive
phenomena on multilayer networks has obviated the fact that social networks
have strong mesoscopic structure represented by different communities of
individuals driven by common interests, or any other social aspect. In this
work, we study the transfer of information in multilayer networks with
community structure. The final goal is to understand and quantify, if the
existence of well-defined community structure at the level of individual
layers, together with the multilayer structure of the whole network, enhances
or deteriorates the diffusion of packets of information.Comment: 13 pages, 6 figure
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