Generalized epidemic process on modular networks

Chung, Kihong; Baek, Yongjoo; Kim, Daniel; Ha, Mina; Jeong, Hawoong

doi:10.1103/physreve.89.052811

Cited by 35 publications

(44 citation statements)

References 26 publications

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“…Finally, we can readily apply the methods discussed here to more general kinds of random networks with Table I are used. locally tree-like structures, such as scale-free networks whose structural heterogeneity would certainly affect the phase diagram and critical behaviors in nontrivial ways [26]. Addressing these issues would broaden our knowledge about universal features of contagion under the influence of cooperative effects.…”

Section: Discussionmentioning

confidence: 99%

“…The model features an infection probability which changes according to the number of contacts with infected individuals. It has been shown that both continuous and discontinuous transitions are possible on regular lattices [3,7] and random networks [3,8,9], with scaling properties belonging to the bond percolation universality class [3,7,9] in the vicinity of critical points. Intermediate tricritical behaviors were also studied by a field-theoretical approach, whose notable differences from the ordinary bond percolation behaviors include the change of the upper critical dimension from 6 to 5 and the breakdown of symmetry * msha@chosun.ac.kr † hjeong@kaist.edu between the percolation probability and the giant cluster size [7].…”

Section: Introductionmentioning

confidence: 99%

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Universality classes of the generalized epidemic process on random networks

Chung

Baek

et al. 2016

Phys. Rev. E

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We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and discontinuous transitions with tricriticality in between. With the help of a comprehensive finite-size scaling theory, we numerically confirm static and dynamic scaling behaviors of the GEP near continuous phase transitions and at tricriticality, which verifies the field-theoretical results of previous studies. We also propose a proper criterion for the discontinuous transition line, which is shown to coincide with the bond percolation threshold.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universality classes of the generalized epidemic process on random networks

Chung

Baek

et al. 2016

Phys. Rev. E

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“…Next we recall discontinuous percolation transitions occurring in generalized contagion models [12][13][14]. Recent studies [15] of a generalized epidemic model [13] revealed that the discontinuous percolation transition turns out to be a hybrid percolation transition (HPT) represented by (1). For this case, a HPT is induced by cluster merging processes.…”

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confidence: 99%

Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents

et al. 2016

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Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a phase transition barely studied before, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent τ in the range 2 < τ (g) ≤ 2.5. This pattern reveals a necessary condition for a hybrid transition in cluster aggregation processes, which is comparable to the power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.PACS numbers: 64.60. De,64.60.ah,89.75.Da Transport or communication systems grow by adding new connections. Often certain constraints are imposed by society and if these constraint involve global knowledge about connectivity, the transition to a percolating system can become first order, as happens for instance when suppressing the spanning cluster, when imposing a cluster size [1] or when favoring the most disconnected sites [2]. Typically this effect is accompanied by the loss of critical scaling making these abrupt transitions less predictable and thus more dangerous. We will show here, that for a specific case, namely a variant of the model introduced in Ref.[3], critical fluctuations and power-law distributions can prevail and for the first time identify a hybrid transition in explosive percolation.Hybrid phase transitions have been observed recently in many complex network systems [4,5]; in these transitions, the order parameter m(t) exhibits behaviors of both first-order and second-order transitions simultaneously aswhere m 0 and r are constants and β is the critical exponent of the order parameter, and t is a control parameter. Examples of such behavior include k-core percolation [6,7], the cascading failure model on interdependent complex networks [8,9], and the Kuramoto synchronization model with a correlation between the natural frequencies and degrees of each node on complex networks [10,11], etc. For the models in [6-9], a critical behavior appears as nodes or links are deleted from a percolating cluster above the percolation threshold until reaching a transition point t c . As t is decreased infinitesimally further as 1/N beyond t c in finite systems, the order parameter decreases suddenly to zero and a first-order phase transition occurs. Thus, a hybrid phase transition occurs at t = t c in the thermodynamic limit. Next we recall discontinuous percolation transitions occurring in generalized contagion models [12][13][14]. Recent studies [15] of a generalized epidemic model [13] revealed that the discontinuous percolation transition turns out to be a hybrid percolation transition (HPT) represented by (1). For this case, a HPT ...

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“…5(b). Finally, for studying the effect of correlations between IETs on the spreading in a simpler setup, we introduce two-step deterministic SI ("2DSI" in short) dynamics [54] as a variation of generalized epidemic processes [57][58][59][60], see Fig. 5(c).…”

Section: Effects Of Correlations Between Iets On Dynamical Procementioning

confidence: 99%

Bursty Time Series Analysis for Temporal Networks

Hiraoka

2019

Computational Social Sciences

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Characterizing bursty temporal interaction patterns of temporal networks is crucial to investigate the evolution of temporal networks as well as various collective dynamics taking place in them. The temporal interaction patterns have been described by a series of interaction events or event sequences, often showing non-Poissonian or bursty nature. Such bursty event sequences can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. The heterogeneities of IETs have been extensively studied in recent years, while the correlations between IETs are far from being fully explored. In this Chapter, we introduce various measures for bursty time series analysis, such as the IET distribution, the burstiness parameter, the memory coefficient, the bursty train sizes, and the autocorrelation function, to discuss the relation between those measures. Then we show that the correlations between IETs can affect the speed of spreading taking place in temporal networks. Finally, we discuss possible research topics regarding bursty time series analysis for temporal networks. * This is a preprint for a chapter to appear in Temporal Network Theory edited by P. Holme and J. Saramäki (https: //www.springer.com/gp/book/9783030234942).

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Generalized epidemic process on modular networks

Cited by 35 publications

References 26 publications

Universality classes of the generalized epidemic process on random networks

Universality classes of the generalized epidemic process on random networks

Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents

Bursty Time Series Analysis for Temporal Networks

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