107,097 research outputs found
Enhancing synchronization in growing networks
Most real systems are growing. In order to model the evolution of real
systems, many growing network models have been proposed to reproduce some
specific topology properties. As the structure strongly influences the network
function, designing the function-aimed growing strategy is also a significant
task with many potential applications. In this letter, we focus on
synchronization in the growing networks. In order to enhance the
synchronizability during the network evolution, we propose the Spectral-Based
Growing (SBG) strategy. Based on the linear stability analysis of
synchronization, we show that our growing mechanism yields better
synchronizability than the existing topology-aimed growing strategies in both
artificial and real-world networks. We also observe that there is an optimal
degree of new added nodes, which means adding nodes with neither too large nor
too low degree could enhance the synchronizability. Furthermore, some topology
measurements are considered in the resultant networks. The results show that
the degree, node betweenness centrality from SBG strategy are more homogenous
than those from other growing strategies. Our work highlights the importance of
the function-aimed growth of the networks and deepens our understanding of it
Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
We study structure, eigenvalue spectra and diffusion dynamics in a wide class
of networks with subgraphs (modules) at mesoscopic scale. The networks are
grown within the model with three parameters controlling the number of modules,
their internal structure as scale-free and correlated subgraphs, and the
topology of connecting network. Within the exhaustive spectral analysis for
both the adjacency matrix and the normalized Laplacian matrix we identify the
spectral properties which characterize the mesoscopic structure of sparse
cyclic graphs and trees. The minimally connected nodes, clustering, and the
average connectivity affect the central part of the spectrum. The number of
distinct modules leads to an extra peak at the lower part of the Laplacian
spectrum in cyclic graphs. Such a peak does not occur in the case of
topologically distinct tree-subgraphs connected on a tree. Whereas the
associated eigenvectors remain localized on the subgraphs both in trees and
cyclic graphs. We also find a characteristic pattern of periodic localization
along the chains on the tree for the eigenvector components associated with the
largest eigenvalue equal 2 of the Laplacian. We corroborate the results with
simulations of the random walk on several types of networks. Our results for
the distribution of return-time of the walk to the origin (autocorrelator)
agree well with recent analytical solution for trees, and it appear to be
independent on their mesoscopic and global structure. For the cyclic graphs we
find new results with twice larger stretching exponent of the tail of the
distribution, which is virtually independent on the size of cycles. The
modularity and clustering contribute to a power-law decay at short return
times
Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
Many natural and social systems develop complex networks, that are usually
modelled as random graphs. The eigenvalue spectrum of these graphs provides
information about their structural properties. While the semi-circle law is
known to describe the spectral density of uncorrelated random graphs, much less
is known about the eigenvalues of real-world graphs, describing such complex
systems as the Internet, metabolic pathways, networks of power stations,
scientific collaborations or movie actors, which are inherently correlated and
usually very sparse. An important limitation in addressing the spectra of these
systems is that the numerical determination of the spectra for systems with
more than a few thousand nodes is prohibitively time and memory consuming.
Making use of recent advances in algorithms for spectral characterization, here
we develop new methods to determine the eigenvalues of networks comparable in
size to real systems, obtaining several surprising results on the spectra of
adjacency matrices corresponding to models of real-world graphs. We find that
when the number of links grows as the number of nodes, the spectral density of
uncorrelated random graphs does not converge to the semi-circle law.
Furthermore, the spectral densities of real-world graphs have specific features
depending on the details of the corresponding models. In particular, scale-free
graphs develop a triangle-like spectral density with a power law tail, while
small-world graphs have a complex spectral density function consisting of
several sharp peaks. These and further results indicate that the spectra of
correlated graphs represent a practical tool for graph classification and can
provide useful insight into the relevant structural properties of real
networks.Comment: 14 pages, 9 figures (corrected typos, added references) accepted for
Phys. Rev.
Valuing flexibility in the migration to flexible-grid networks
Increasing network demand is expected to put pressure on the available capacity in core networks. Flexible optical networking can now be installed to increase network capacity in light of future traffic demands. However, this technology is still in its infancy and might lack the full functionality that may appear within a few years. When replacing core network equipment, it is therefore important to make the right investment decision between upgrading toward flexible-grid or fixed-grid equipment. This paper researches various installation options using a techno-economic analysis, extended with real option insights, showing the impact of uncertainty and flexibility on the investment decision. By valuing the different options, a correct investment decision can be made
Topological resilience in non-normal networked systems
The network of interactions in complex systems, strongly influences their
resilience, the system capability to resist to external perturbations or
structural damages and to promptly recover thereafter. The phenomenon manifests
itself in different domains, e.g. cascade failures in computer networks or
parasitic species invasion in ecosystems. Understanding the networks
topological features that affect the resilience phenomenon remains a
challenging goal of the design of robust complex systems. We prove that the
non-normality character of the network of interactions amplifies the response
of the system to exogenous disturbances and can drastically change the global
dynamics. We provide an illustrative application to ecology by proposing a
mechanism to mute the Allee effect and eventually a new theory of patterns
formation involving a single diffusing species
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