Université de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, Lyon, 69364, France.
Department of Network and Data Science, Central European University, Vienna, A-1100, Austria.
Nat Commun. 2021 Jan 8;12(1):133. doi: 10.1038/s41467-020-20398-4.
Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. Here we develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.
突发性是指交互事件在时间上呈非均匀分布的趋势，它对物理和社会系统中的信息传播至关重要。然而，缺乏一个能够捕捉突发性对一般动力学影响的分析框架。在这里，我们开发了一个主方程形式来研究具有突发特性的时变网络上的级联过程，这些突发特性可以通过更新过程来建模。通过数值和数据驱动的模拟，我们描述了异质时间相互作用与阈值驱动和流行病传播模型之间的相互作用。我们发现，增加事件间时间方差可以加速和减缓阈值模型的传播，但只能减缓流行病的传播。当考虑到不同事件间时间分布的偏度时，传播时间会崩溃到一个通用的曲线上。我们的框架揭示了一般扩散机制和潜在的时变网络结构之间的深刻而微妙的联系，这影响了广泛的网络现象，从自旋相互作用到流行病的传播和语言动态。
