Cascades on a class of clustered random networks

Hackett, Adam; Melnik, Sergey; Gleeson, James P.

doi:10.1103/physreve.83.056107

Cited by 113 publications

(151 citation statements)

References 55 publications

(155 reference statements)

Supporting

Mentioning

146

Contrasting

Unclassified

Order By: Relevance

“…The simplest case of an avalanche corresponds to a branching process [14,15], first studied by Galton and Watson [3], which can be considered as an avalanche propagating in a tree network. Various generalizations to the case where avalanches propagate in a more general network have been considered recently [13,[16][17][18], and related problems such as the distribution of cluster size in percolation models [19,20] and selforganized criticality in the "sandpile" model [21] have been studied. In contrast to these previous studies, we develop a theory of avalanche size and duration on complex networks that, instead of using some form of mean field analysis, explicitly includes the network topology.…”

Section: Introductionmentioning

confidence: 99%

Statistical properties of avalanches in networks

et al. 2012

View full text Add to dashboard Cite

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated 'excitation' of a network node, which may, with some probability, then stimulate subsequent firings of the nodes to which it is connected, resulting in a cascade of firings. This type of process is relevant to a wide variety of situations, including neuroscience, cascading failures on electrical power grids, and epidemology. We find that the statistics of avalanches can be characterized in terms of the largest eigenvalue and corresponding eigenvector of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches. Our results apply to individual networks (rather than network ensembles) and provide expressions for the distributions of size and duration of avalanches starting at particular nodes in the network. These findings might find application in the analysis of branching processes in networks, such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of size and duration of neuronal avalanches), are robust to complex underlying network topologies.

show abstract

Section: Introductionmentioning

confidence: 99%

Statistical properties of avalanches in networks

et al. 2012

View full text Add to dashboard Cite

show abstract

“…The differences in p c can be attributed to the broadening of P (k) in the case of doubly Poisson distribution. Note that for site percolation on a sinlge clustered network, larger clustering coefficient leads to higher critical shreshold [28,38]. Here for a system of two interdependent networks, the general trend is simliar, that for both degree distributions, p c increases as clustering coefficient being larger.…”

Section: Fixed Degree Distributionmentioning

confidence: 76%

“…Here we consider another kind of joint distribution P st proposed by Hackett et al [38,39], which preserves the total degree distribution P (k) for different clustering coefficients. We set…”

Section: Fixed Degree Distributionmentioning

confidence: 99%

Robustness of a partially interdependent network formed of clustered networks

et al. 2014

View full text Add to dashboard Cite

Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of clustering on the robustness of coupled networks received very little attention. Only the case of a pair of fully coupled networks with clustering has been studied recently. Here we generalize the study of clustering of a fully coupled pair of networks to the study of partially interdependent network of networks with clustering within the network components. We show both analytically and numerically, how clustering within the networks, affects the percolation properties of interdependent networks, including percolation threshold, size of giant component and critical coupling point where first order phase transition changes to second order phase transition as the coupling between the networks reduces. We study two types of clustering: one type proposed by Newman [25] where the average degree is kept constant while changing the clustering and the other proposed by Hackett et al. [38] where the degree distribution is kept constant. The first type of clustering is treated both analytically and numerically while the second one is treated only numerically.

show abstract

“…Rigorous results (for the classical SIR epidemic) were obtained by Britton et al [6] and by Bollobás et al [5], but the random graphs considered are such that their asymptotic degree distributions are respectively Poisson and mixed Poisson. Recently, Hackett et al [13] studied by heuristic means the contagion model on random graphs with overlapping communities, i.e. with nodes that can belong to several cliques.…”

Section: Introductionmentioning

confidence: 99%

Contagions in random networks with overlapping communities

Coupechoux

Lelarge²

2015

Adv. Appl. Probab.

View full text Add to dashboard Cite

We consider a threshold epidemic model on a clustered random graph model obtained from local transformations in an alternating branching process that approximates a bipartite graph. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of his/her infected neighbors exceeds the threshold q of the epidemic. In our random graph model, each individual can belong to several communities. The distributions for the community sizes and the number of communities an individual belongs to are arbitrary. We consider the case where the epidemic starts from a single individual, and we prove a phase transition (when the parameter q of the model varies) for the appearance of a cascade, i.e. when the epidemic can be propagated to an infinite part of the population. More precisely, we show that our epidemic is entirely described by a multi-type (and alternating) branching process, and then we apply Sevastyanov's theorem about the phase transition of multi-type Galton-Watson branching processes. In addition, we compute the entries of the mean progeny matrix corresponding to the epidemic. The phase transition for the contagion is given in terms of the largest eigenvalue of this matrix.

show abstract

Cascades on a class of clustered random networks

Cited by 113 publications

References 55 publications

Statistical properties of avalanches in networks

Statistical properties of avalanches in networks

Robustness of a partially interdependent network formed of clustered networks

Contagions in random networks with overlapping communities

Contact Info

Product

Resources

About