Complex contagions and hybrid phase transitions

Miller, Joel C.

doi:10.1093/comnet/cnv021

Cited by 17 publications

(8 citation statements)

References 41 publications

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“…The requirement of multiple interactions for adoption was first implemented theoretically by Granovetter via behavioural thresholds, namely 'the number or proportion of others who must make one decision before a given actor does so' [6]. Following this idea various agent-based network models have been introduced and analysed by Watts and others [1,[24][25][26][27][28][29][30][31] in order to understand the properties of threshold-driven social contagion.…”

Section: Introductionmentioning

confidence: 99%

Service Adoption Spreading in Online Social Networks

Iñiguez¹,

Ruan²,

Kaski³

et al. 2018

Computational Social Sciences

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The collective behaviour of people adopting an innovation, product or online service is commonly interpreted as a spreading phenomenon throughout the fabric of society. This process is arguably driven by social influence, social learning and by external effects like media. Observations of such processes date back to the seminal studies by Rogers and Bass, and their mathematical modelling has taken two directions: One paradigm, called simple contagion, identifies adoption spreading with an epidemic process. The other one, named complex contagion, is concerned with behavioural thresholds and successfully explains the emergence of large cascades of adoption resulting in a rapid spreading often seen in empirical data. The observation of real world adoption processes has become easier lately due to the availability of large digital social network and behavioural datasets. This has allowed simultaneous study of network structures and dynamics of online service adoption, shedding light on the mechanisms and external effects that influence the temporal evolution of behavioural or innovation adoption. These advancements

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Section: Introductionmentioning

confidence: 99%

Service Adoption Spreading in Online Social Networks

Iñiguez¹,

Ruan²,

Kaski³

et al. 2018

Computational Social Sciences

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“…However, associating the number of steps in the pruning process with time t reveals a process exhibiting complex dynamics above, below, and at the k-core percolation threshold. Understanding the k-core pruning process and accompanying structural changes can shed light on various critical phenomena, such as the jamming transition, the rigidity percolation, glassy dynamics [15,16], complex contagion [17], mass extinction [18], avalanches in neuronal networks [19], and many others. Furthermore, the k-core pruning process is one of the simplest examples of dynamic processes associated with hybrid phase transitions, sharing, for example, some common properties with cascade failures in interdependent networks that have recently received significant attention in the literature [6,12,[20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Critical Dynamics of thek-Core Pruning Process

et al. 2015

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We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure and solve them numerically and, in the critical regime of the process, analytically. We show that the pruning process exhibits three different behaviors depending on whether the mean degree hqi of the initial network is above, equal to, or below the threshold hqi c corresponding to the emergence of the giant k-core. We find that above the threshold the network relaxes exponentially to the k-core. The system manifests the phenomenon known as "critical slowing-down," as the relaxation time diverges when hqi tends to hqi c . At the threshold, the dynamics become critical, characterized by a power-law relaxation (∝ 1=t 2 ). Below the threshold, a long-lasting transient process (a "plateau" stage) occurs. This transient process ends with a collapse in which the entire network disappears completely. The duration of the process diverges when hqi → hqi c . We show that the critical dynamics of the pruning are determined by branching processes of spreading damage. Clusters of nodes of degree exactly k are the evolving substrate for these branching processes. Our theory completely describes this branching cascade of damage in uncorrelated networks by providing the time-dependent distribution function of branching. These theoretical results are supported by our simulations of the k-core pruning in Erdős-Rényi graphs.

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“…Similar to the spreading of health behavior [136,140,141], global cascades occur more easily on clustered networks than on nonclustered networks [158]. Hackett et al [159] explored cascades on clustered networks produced by the configuration model with adjustable clustering [70], and found that there exists a range of k in which increasing the clustering of the network results in an increase in the mean cascade size, whereas outside of this range it will decrease the mean cascade size [160]. Hackett and Gleeson [161] further explored cascade phenomena on highly clustered clique-based graphs [162] and obtained a closed-form expression for the final fraction of active nodes within a clique of arbitrary size.…”

Section: Threshold Modelmentioning

confidence: 99%

Coevolution spreading in complex networks

et al. 2019

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a b s t r a c tThe propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

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Complex contagions and hybrid phase transitions

Cited by 17 publications

References 41 publications

Service Adoption Spreading in Online Social Networks

Service Adoption Spreading in Online Social Networks

Critical Dynamics of thek-Core Pruning Process

Coevolution spreading in complex networks

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