Synchronization in weighted scale-free networks with degree–degree correlation

Sorrentino, Francesco; Bernardo, Mario di; Huerta-Cuéllar, G.; Boccaletti, Stefano

doi:10.1016/j.physd.2006.09.030

Cited by 82 publications

(68 citation statements)

References 26 publications

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“…Specifically in [26], the network synchronizability has been shown to be enhanced as the network becomes more disassortative (i.e. r decreases) for both systems in class I and II (namely, what is observed is that the second smallest eigenvalue varies sensibly with r, while the largest one is weakly influenced by variations of the network degree correlation).…”

Section: Effects Of Degree Correlationmentioning

confidence: 93%

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Effects of the network structural properties on its controllability

Sorrentino

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In a recent paper, it has been suggested that the controllability of a diffusively coupled complex network, subject to localized feedback loops at some of its vertices, can be assessed by means of a Master Stability Function approach, where the network controllability is defined in terms of the spectral properties of an appropriate Laplacian matrix. Following that approach, a comparison study is reported here among different network topologies in terms of their controllability. The effects of heterogeneity in the degree distribution, as well as of degree correlation and community structure, are discussed.Comment: Also available online at: http://link.aip.org/link/?CHA/17/03310

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Section: Effects Of Degree Correlationmentioning

confidence: 93%

“…The effects of degree correlation on the network synchronizability have been studied in [26]. Specifically in [26], the network synchronizability has been shown to be enhanced as the network becomes more disassortative (i.e.…”

Section: Effects Of Degree Correlationmentioning

confidence: 99%

Effects of the network structural properties on its controllability

Sorrentino

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In complex networks various aspects of this have been the focus of much study including robustness (28,29), controllability (30), and synchronization (31). Much current research focuses on the indegree and out-degree correlations of the dependency links between networks.…”

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confidence: 99%

Breakdown of interdependent directed networks

Liu

Stanley

Gao

2016

Proc. Natl. Acad. Sci. U.S.A.

138

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Increasing evidence shows that real-world systems interact with one another via dependency connectivities. Failing connectivities are the mechanism behind the breakdown of interacting complex systems, e.g., blackouts caused by the interdependence of power grids and communication networks. Previous research analyzing the robustness of interdependent networks has been limited to undirected networks. However, most real-world networks are directed, their in-degrees and out-degrees may be correlated, and they are often coupled to one another as interdependent directed networks. To understand the breakdown and robustness of interdependent directed networks, we develop a theoretical framework based on generating functions and percolation theory. We find that for interdependent Erd} os-Rényi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions. We also find that the percolation behavior of interdependent directed scale-free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness: the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correlations, confirming our theoretical analysis.interdependent networks | directed networks | degree correlations | percolation theory

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“…Generally speaking, the case of β = 1, with the weights of the incoming links at each vertex summing to -1 (so that L ii = 1 ∀i), is of particular interest in that all the networks satisfying this constraint, become directly comparable among themselves, in terms of their spectral properties ] (see also [Sorrentino, di Bernardo, Cuellar & Boccaletti 2006].) In fact, according to the Gerschgorin's circle theorem, all the eigenvalues (λ j = λ r j +jλ i j , j = 1, 2, ..., N ) of these network are known to belong to a bounded region of the complex plane, and specifically the circle of radius 1, centered at 1 on the real axis .…”

Section: Weighed Networkmentioning

confidence: 99%

Synchronizability and Synchronization Dynamics of Weighed and Unweighed Scale Free Networks With Degree Mixing

Sorrentino

Bernardo

Garofalo

2007

Int. J. Bifurcation Chaos

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We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators.We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power law exponent γ and the degree correlation coefficient r. Using an appropriate construction algorithm based on clustering the network vertices in p classes according to their degrees, we construct networks with an assigned power law distribution but changing degree correlation properties. We find that the network synchronizability improves when the network becomes disassortative, i.e. when nodes with low degree are more likely to be connected to nodes with higher degree. We consider the case of both weighed and unweighed networks. The analytical results reported in the paper are then confirmed by a set of numerical observations obtained on weighed and unweighed networks of nonlinear Rössler oscillators. Using a nonlinear optimization strategy we also show that negative degree correlation is an emerging property of networks when synchronizability is to be optimized. This suggests that negative degree correlation observed experimentally in a number of physical and biological networks might be motivated by their need to synchronize better.

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Synchronization in weighted scale-free networks with degree–degree correlation

Cited by 82 publications

References 26 publications

Effects of the network structural properties on its controllability

Effects of the network structural properties on its controllability

Breakdown of interdependent directed networks

Synchronizability and Synchronization Dynamics of Weighed and Unweighed Scale Free Networks With Degree Mixing

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