Instability of scale-free networks under node-breaking avalanches

Moreno, Yamir; Gómez, J.; Pacheco, A. F.

doi:10.1209/epl/i2002-00442-2

Cited by 216 publications

(127 citation statements)

References 25 publications

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“…We didn't discuss the distribution of the number of the shortest paths passing through a vertex, which has a power-law form in scale-free networks [235,236], and many other interesting problems (see, e.g., Refs. [237][238][239][240][241][242][243][244][245][246][247][248][249][250][251]). After this review had been submitted, we learned about the review of Albert and Barabási on the statistical mechanics of networks under preparation [252].…”

Section: Discussionmentioning

confidence: 99%

Evolution of networks

Dorogovtsev¹,

Mendes²

2002

Advances in Physics

2,606

1,850

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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -a feature known as the "smallworld" effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc. CONTENTS

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Section: Discussionmentioning

confidence: 99%

Evolution of networks

Dorogovtsev¹,

Mendes²

2002

Advances in Physics

2,606

1,850

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“…The procedure enables us to study overload breakdown triggered by the redistribution (and increase) of load in a growing network. This is in contrast to earlier models of cascading breakdown phenomena, all dealing with vertex breakdown, that has taken a fixed network as their starting point [12,13]. * Electronic address: holme@tp.umu.se…”

Section: Introductionmentioning

confidence: 87%

Edge overload breakdown in evolving networks

Holme

2002

Phys. Rev. E

144

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We investigate growing networks based on Barabási and Albert's algorithm for generating scalefree networks, but with edges sensitive to overload breakdown. The load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabási and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.

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“…An important question for many real-world situations is how attacks affect the functions of a network when the flow of information or other physical quantity in the network are taken into consideration. In particular, the removal of nodes changes the balance of flows and may trigger a cascading failure [31][32][33][34], as the one that happened on August 10, 1996 in the western U.S. power grid [35,36]. A simple model has been recently introduced [14] for cascades of overload failures in complex networks.…”

Section: Attack-induced Cascades In Complex Networkmentioning

confidence: 99%

Attacks and Cascades in Complex Networks

Lai

Motter

Nishikawa

2004

Lecture Notes in Physics

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Abstract. This paper reviews two problems in the security of complex networks: cascades of overload failures on nodes and range-based attacks on links. Cascading failures have been reported for numerous networks and refer to the subsequent failure of other parts of the network induced by the failure of or attacks on only a few nodes. We investigate a mechanism leading to cascades of overload failures in complex networks by constructing a simple model incorporating the flow of physical quantities in the network. The second problem is motivated by the fact that most existing works on security of complex networks consider attacks on nodes rather than on links. We address attacks on links. Our investigation leads to the finding that many scale-free networks are more sensitive to attacks on short-range than on long-range links. Besides its importance concerning network security, our result has the unexpected implication that the small-world phenomenon in these scale-free networks is mainly due to short-range links.

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Instability of scale-free networks under node-breaking avalanches

Cited by 216 publications

References 25 publications

Evolution of networks

Evolution of networks

Edge overload breakdown in evolving networks

Attacks and Cascades in Complex Networks

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