Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading

Karsai, Márton; Iñiguez, Gerardo; Kikas, Riivo; Kaski, Kimmo; Kertész, János

doi:10.1038/srep27178

Cited by 68 publications

(78 citation statements)

References 57 publications

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“…We solve for our model using the approximate master equation (AME) formalism [43,44]. Similar to earlier solutions [10,14,16], at time t, the density of infected nodes ρ and the average probability ν j that a j-type neighbor of a susceptible node is infected are governed by the system of coupled differential equations,ν…”

Section: Resultsmentioning

confidence: 99%

Reentrant phase transitions in threshold driven contagion on multiplex networks

Unicomb

Iñiguez

Kertész³

et al. 2019

Phys. Rev. E

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Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a novel theoretical explanation for the observation of large scale contagion in highly connected but heterogeneous networks.

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Section: Resultsmentioning

confidence: 99%

Reentrant phase transitions in threshold driven contagion on multiplex networks

Unicomb

Iñiguez

Kertész³

et al. 2019

Phys. Rev. E

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“…While some empirical networks consist of a single connected component such as transportation networks and brain networks [47], other networks consist of many isolated components of various sizes such as adoption of innovations or products networks [48] and mobile phone calling networks [49]. The distribution of sizes of these components has been studied in the context of subcritical networks and provides a useful characterization of the network structure [24].…”

Section: Discussionmentioning

confidence: 99%

Generating random networks that consist of a single connected component with a given degree distribution

et al. 2019

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We present a method for the construction of ensembles of random networks that consist of a single connected component with a given degree distribution. This approach extends the construction toolbox of random networks beyond the configuration model framework, in which one controls the degree distribution but not the number of components and their sizes. Unlike configuration model networks, which are completely uncorrelated, the resulting single-component networks exhibit degree-degree correlations. Moreover, they are found to be disassortative, namely high-degree nodes tend to connect to low-degree nodes and vice versa. We demonstrate the method for singlecomponent networks with ternary, exponential and power-law degree distributions. PACS numbers: 64.60.aq,89.75.Da 1 I. INTRODUCTIONNetwork models provide a useful description of a broad range of phenomena in the natural sciences and engineering as well as in the economic and social sciences. This realization has stimulated increasing interest in the structure of complex networks, and in the dynamical processes that take place on them [1-9]. One of the central lines of inquiry has been concerned with the existence of a giant connected component that is extensive in the network size. In the case of Erdős-Rényi (ER) networks, the critical parameters for the emergence of a giant component in the thermodynamic limit were identified and the fraction of nodes that reside in the giant component was determined [10][11][12][13]. These studies were later extended to the broader class of configuration model networks [14,15]. The configuration model framework enables one to construct an ensemble of random networks whose degree sequences are drawn from a desired degree distribution, with no degree-degree correlations. The resulting network ensemble is a maximum entropy ensemble under the condition of the given degree distribution. A simple example of a configuration model network is the random regular graph, in which all the nodes are of the same degree, k = c. For random regular graphs with c ≥ 3 the giant component encompasses the whole network [16]. However, in general, configuration model networks often exhibit a coexistence between a giant component, which is extensive in the network size, and many finite components, which are non-extensive trees. This can be exemplified by the case of ER networks, which exhibit a Poisson degree distribution of the formwhere c = K is the mean degree. ER networks with 0 < c < 1 consist of finite tree components. At c = 1 there is a percolation transition, above which the network exhibits a coexistence between the giant component and the finite components. In the asymptotic limit, the size of the giant component is N 1 = gN, where N is the size of the whole network and the parameter g = g(c), which vanishes for c ≤ 1, increases monotonically for c > 1. At c = ln N there is a second transition, above which the giant component encompasses the entire network [16]. In the range of 1 < c < ln N, where the giant and finite components coexist, the...

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“…In this case, θ X (∞) = 1 is not a solution of Eq. (15). At the critical point of first-order phase transition, the condition…”

Section: Theorymentioning

confidence: 99%

“…In the real world, the influences of network neighbors and the tendency for any individual to adopt certain behavior can be highly non-uniform. There is empirical evidence that individuals and their social contacts tend to play heterogeneous roles in contagion [14,15]. For example, regardless of the nature of the behavior, there always exist certain individuals who are * shimin.cai81@gmail.com reluctant to accept or adopt the behavior.…”

Section: Introductionmentioning

confidence: 99%

Close and ordinary social contacts: How important are they in promoting large-scale contagion?

Cui

Wang²,

Cai

et al. 2018

Phys. Rev. E

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An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members, etc., and ordinary contacts from encounters with strangers. Typically, social reinforcement occurs for close contacts. Taking into account both types of contacts, we develop a contact-based model for social contagion. We find that, associated with the spreading dynamics, for random networks there is coexistence of continuous and discontinuous phase transitions, but for heterogeneous networks the transition is continuous. We also find that ordinary contacts play a crucial role in promoting large scale spreading, and the number of close contacts determines not only the nature of the phase transitions but also the value of the outbreak threshold in random networks. For heterogeneous networks from the real world, the abundance of close contacts affects the epidemic threshold, while its role in facilitating the spreading depends on the adoption threshold assigned to it. We uncover two striking phenomena. First, a strong interplay between ordinary and close contacts is necessary for generating prevalent spreading. In fact, only when there are propagation paths of reasonable length which involve both close and ordinary contacts are large scale outbreaks of social contagions possible. Second, abundant close contacts in heterogeneous networks promote both outbreak and spreading of the contagion through the transmission channels among the hubs, when both values of the threshold and transmission rate among ordinary contacts are small. We develop a theoretical framework to obtain an analytic understanding of the main findings on random networks, with support from extensive numerical computations. Overall, ordinary contacts facilitate spreading over the entire network, while close contacts determine the way by which outbreaks occur, i.e., through a second or first order phase transition. These results provide quantitative insights into how certain social behaviors can emerge and become prevalent, which has potential implications not only to social science, but also to economics and political science.

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Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading

Cited by 68 publications

References 57 publications

Reentrant phase transitions in threshold driven contagion on multiplex networks

Reentrant phase transitions in threshold driven contagion on multiplex networks

Generating random networks that consist of a single connected component with a given degree distribution

Close and ordinary social contacts: How important are they in promoting large-scale contagion?

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