Cascades on correlated and modular random networks

被引：166

作者：

Gleeson, James P. ^{[1
]}

机构：

[1] Univ Limerick, Dept Math & Stat, Limerick, Ireland

来源：

PHYSICAL REVIEW E | 2008年 / 77卷 / 04期

关键词：

D O I：

10.1103/PhysRevE.77.046117

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

An analytical approach to determining the mean avalanche size in a broad class of dynamical models on random networks is introduced. Previous results on percolation transitions and epidemic sizes are shown to be special cases of the method. The time-dependence of cascades and extensions to networks with community structure or degree-degree correlations are discussed. Analytical results for the rate of spread of innovations in a modular network and for the size of k cores in networks with degree-degree correlations are confirmed with numerical simulations.

引用

页数：10

共 40 条

[1] Error and attack tolerance of complex networks [J].

Albert, R ;

Jeong, H ;

Barabási, AL .

NATURE, 2000, 406 (6794) :378-382

[2] Complex networks - Augmenting the framework for the study of complex systems [J].

Amaral, LAN ;

Ottino, JM .

EUROPEAN PHYSICAL JOURNAL B, 2004, 38 (02) :147-162

[3] Evolutionary dynamics on degree-heterogeneous graphs [J].

Antal, T. ;

Redner, S. ;

Sood, V. .

PHYSICAL REVIEW LETTERS, 2006, 96 (18)

[4] Complex networks: Structure and dynamics [J].

Boccaletti, S. ;

Latora, V. ;

Moreno, Y. ;

Chavez, M. ;

Hwang, D. -U. .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2006, 424 (4-5) :175-308

[5] Network robustness and fragility: Percolation on random graphs [J].

Callaway, DS ;

Newman, MEJ ;

Strogatz, SH ;

Watts, DJ .

PHYSICAL REVIEW LETTERS, 2000, 85 (25) :5468-5471

[6] A model of Internet topology using k-shell decomposition [J].

Carmi, Shai ;

Havlin, Shlomo ;

Kirkpatrick, Scott ;

Shavitt, Yuval ;

Shir, Eran .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2007, 104 (27) :11150-11154

[7] Resilience of the Internet to random breakdowns [J].

Cohen, R ;

Erez, K ;

ben-Avraham, D ;

Havlin, S .

PHYSICAL REVIEW LETTERS, 2000, 85 (21) :4626-4628

[8] Percolation critical exponents in scale-free networks [J].

Cohen, R ;

ben-Avraham, D ;

Havlin, S .

PHYSICAL REVIEW E, 2002, 66 (03) :1-036113

[9] Model for cascading failures in complex networks [J].

Crucitti, P ;

Latora, V ;

Marchiori, M .

PHYSICAL REVIEW E, 2004, 69 (04) :4

[10] Zero-temperature hysteresis in the random-field Ising model on a Bethe lattice [J].

Dhar, D ;

Shukla, P ;

Sethna, JP .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1997, 30 (15) :5259-5267

← 1 2 3 4 →