Edge overload breakdown in evolving networks

Holme, Petter

doi:10.1103/physreve.66.036119

Cited by 144 publications

(58 citation statements)

References 35 publications

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“…These point to the facts that most networks grow continuously by adding new nodes, which are preferentially attached to existing nodes with large number of neighbors. The subsequent researches on various processes taking place upon complex networks, such as percolation [82,87,88,89,90,91,92,93,94,95,96,97,98], epidemic processes [99,100,101,102,103,104,105,106], cascade processes [107,108,109,110,111,112,113,114,115] and so on, indicate that the scale-free degree distribution plays the most crucial role rather than smallworld effect. Therefore, in the recent two or three years, the study of modelling complex networks focuses on revealing the underlying mechanism of power-law degree distribution.…”

Section: Introductionmentioning

confidence: 99%

Maximal planar networks with large clustering coefficient and power-law degree distribution

2005

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In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called Random Apollonian Networks(RAN) as they can be considered as a variation of Apollonian networks. We obtain the analytic results of power-law exponent γ = 3 and clustering coefficient C = 46 3 − 36ln 3 2 ≈ 0.74, which agree very well with the simulation results. We prove that the increasing tendency of average distance of RAN is a little slower than the logarithm of the number of nodes in RAN. Since most reallife networks are both scale-free and small-world networks, RAN may perform well in mimicking the reality. The RAN possess hierarchical structure as C(k) ∼ k −1 that in accord with the observations of many real-life networks. In addition, we prove that RAN are maximal planar networks, which are of particular practicability for layout of printed circuits and so on. The percolation and epidemic spreading process are also studies and the comparison between RAN and Barabási-Albert(BA) as well as Newman-Watts(NW) networks are shown. We find that, when the network order N (the total number of nodes) is relatively small(as N ∼ 10 4 ), the performance of RAN under intentional attack is not sensitive to N , while that of BA networks is much affected by N . And the diseases spread slower in RAN than BA networks during the outbreaks, indicating that the large clustering coefficient may slower the spreading velocity especially in the outbreaks.

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Section: Introductionmentioning

confidence: 99%

Maximal planar networks with large clustering coefficient and power-law degree distribution

2005

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“…Moreover, when the network becomes unconnected, E is a better quantity than L to describe the system. Different approaches to study the vulnerability of a network have been proposed by Goh et al [43], Kim et al [284], Motter et al [285], Holme [286,287], and Latora and Marchiori [34].…”

Section: Numerical Resultsmentioning

confidence: 99%

Complex networks: Structure and dynamics

et al. 2006

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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks' dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

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“…Models of cascading failure have also been studied by Holme and Kim [195,199], by Moreno et al [297,298] and by Motter and Lai [305]. In the model of Holme and Kim, for instance, load on a vertex is quantified by the betweenness centrality of the vertex (see Sec.…”

Section: A Percolation Theory and Network Resiliencementioning

confidence: 99%

The Structure and Function of Complex Networks

Newman¹

2003

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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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Edge overload breakdown in evolving networks

Cited by 144 publications

References 35 publications

Maximal planar networks with large clustering coefficient and power-law degree distribution

Maximal planar networks with large clustering coefficient and power-law degree distribution

Complex networks: Structure and dynamics

The Structure and Function of Complex Networks

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