在具有社区结构的网络中建模扩散：一种多类型分支过程方法
Modeling diffusion in networks with communities: a multitype branching process approach
AI总结：
本文提出利用多类型分支过程方法，在具有社区结构的网络中建模和分析扩散过程，通过度分布计算传播动态特征，并验证了其在不同网络结构中的有效性。
摘要：
复杂网络中扩散动力学的研究广泛开展，以理解信息、疾病或行为等实体在互联环境中的传播方式。复杂网络往往具有社区结构，需要分析具有社区结构的网络上扩散过程的工具。本文开发了使用多类型分支过程的理论工具，以建模和分析在具有社区结构的广泛网络上遵循简单传染机制的扩散过程。我们展示了如何通过有限的网络信息——社区内和社区间的度分布——计算传播动态的标准统计特征，如灭绝概率、危险函数和级联大小分布。这些特性不仅可以估计整个网络，还可以分别估计每个社区。此外，我们估计了从一个社区传播到另一个社区的传播概率，其中传播尚未发生。我们通过将其应用于两种特定示例——随机块模型和具有社区结构的对数正态网络——来展示框架的准确性。我们展示了初始播种位置如何影响重尾网络上观察到的级联大小分布，并表明我们的框架能够准确捕捉这种影响。
英文摘要：
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools to analyze diffusion processes on networks with communities are needed. In this paper, we develop theoretical tools using multi-type branching processes to model and analyze diffusion processes, following a simple contagion mechanism, across a broad class of networks with community structure. We show how, by using limited information about the network -- the degree distribution within and between communities -- we can calculate standard statistical characteristics of propagation dynamics, such as the extinction probability, hazard function, and cascade size distribution. These properties can be estimated not only for the entire network but also for each community separately. Furthermore, we estimate the probability of spread crossing from one community to another where it is not currently spreading. We demonstrate the accuracy of our framework by applying it to two specific examples: the Stochastic Block Model and a log-normal network with community structure. We show how the initial seeding location affects the observed cascade size distribution on a heavy-tailed network and that our framework accurately captures this effect.
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