94,508 research outputs found
Enhancing complex-network synchronization
Heterogeneity in the degree (connectivity) distribution has been shown to
suppress synchronization in networks of symmetrically coupled oscillators with
uniform coupling strength (unweighted coupling). Here we uncover a condition
for enhanced synchronization in directed networks with weighted coupling. We
show that, in the optimum regime, synchronizability is solely determined by the
average degree and does not depend on the system size and the details of the
degree distribution. In scale-free networks, where the average degree may
increase with heterogeneity, synchronizability is drastically enhanced and may
become positively correlated with heterogeneity, while the overall cost
involved in the network coupling is significantly reduced as compared to the
case of unweighted coupling.Comment: 4 pages, 3 figure
Thesaurus as a complex network
A thesaurus is one, out of many, possible representations of term (or word)
connectivity. The terms of a thesaurus are seen as the nodes and their
relationship as the links of a directed graph. The directionality of the links
retains all the thesaurus information and allows the measurement of several
quantities. This has lead to a new term classification according to the
characteristics of the nodes, for example, nodes with no links in, no links
out, etc. Using an electronic available thesaurus we have obtained the incoming
and outgoing link distributions. While the incoming link distribution follows a
stretched exponential function, the lower bound for the outgoing link
distribution has the same envelope of the scientific paper citation
distribution proposed by Albuquerque and Tsallis. However, a better fit is
obtained by simpler function which is the solution of Ricatti's differential
equation. We conjecture that this differential equation is the continuous limit
of a stochastic growth model of the thesaurus network. We also propose a new
manner to arrange a thesaurus using the ``inversion method''.Comment: Contribution to the Proceedings of `Trends and Perspectives in
Extensive and Nonextensive Statistical Mechanics', in honour of Constantino
Tsallis' 60th birthday (submitted Physica A
Investigation of a Protein Complex Network
The budding yeast {\it Saccharomyces cerevisiae} is the first eukaryote whose
genome has been completely sequenced. It is also the first eukaryotic cell
whose proteome (the set of all proteins) and interactome (the network of all
mutual interactions between proteins) has been analyzed. In this paper we study
the structure of the yeast protein complex network in which weighted edges
between complexes represent the number of shared proteins. It is found that the
network of protein complexes is a small world network with scale free behavior
for many of its distributions. However we find that there are no strong
correlations between the weights and degrees of neighboring complexes. To
reveal non-random features of the network we also compare it with a null model
in which the complexes randomly select their proteins. Finally we propose a
simple evolutionary model based on duplication and divergence of proteins.Comment: 19 pages, 9 figures, 1 table, to appear in Euro. Phys. J.
Complex network analysis and nonlinear dynamics
This chapter aims at reviewing complex network and nonlinear dynamical
models and methods that were either developed for or applied to socioeconomic
issues, and pertinent to the theme of New Economic Geography. After an introduction
to the foundations of the field of complex networks, the present summary
introduces some applications of complex networks to economics, finance, epidemic
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issue
Phase transitions in a complex network
We study a mean field model of a complex network, focusing on edge and
triangle densities. Our first result is the derivation of a variational
characterization of the entropy density, compatible with the infinite node
limit. We then determine the optimizing graphs for small triangle density and a
range of edge density, though we can only prove they are local, not global,
maxima of the entropy density. With this assumption we then prove that the
resulting entropy density must lose its analyticity in various regimes. In
particular this implies the existence of a phase transition between distinct
heterogeneous multipartite phases at low triangle density, and a phase
transition between these phases and the disordered phase at high triangle
density.Comment: Title of previous version was `A mean field analysis of the
fluid/solid phase transition
Quantum Google in a Complex Network
We investigate the behavior of the recently proposed quantum Google
algorithm, or quantum PageRank, in large complex networks. Applying the quantum
algorithm to a part of the real World Wide Web, we find that the algorithm is
able to univocally reveal the underlying scale-free topology of the network and
to clearly identify and order the most relevant nodes (hubs) of the graph
according to their importance in the network structure. Moreover, our results
show that the quantum PageRank algorithm generically leads to changes in the
hierarchy of nodes. In addition, as compared to its classical counterpart, the
quantum algorithm is capable to clearly highlight the structure of secondary
hubs of the network, and to partially resolve the degeneracy in importance of
the low lying part of the list of rankings, which represents a typical
shortcoming of the classical PageRank algorithm. Complementary to this study,
our analysis shows that the algorithm is able to clearly distinguish scale-free
networks from other widespread and important classes of complex networks, such
as Erd\H{o}s-R\'enyi networks and hierarchical graphs. We show that the ranking
capabilities of the quantum PageRank algorithm are related to an increased
stability with respect to a variation of the damping parameter that
appears in the Google algorithm, and to a more clearly pronounced power-law
behavior in the distribution of importance among the nodes, as compared to the
classical algorithm. Finally, we study to which extent the increased
sensitivity of the quantum algorithm persists under coordinated attacks of the
most important nodes in scale-free and Erd\H{o}s-R\'enyi random graphs
- …