论文标题
一种生成功能方法，用于建模具有多类分支过程的聚类网络上的复杂传播
A generating-function approach to modelling complex contagion on clustered networks with multi-type branching processes
论文作者
论文摘要
了解复杂网络拓扑上的级联流程对于建模疾病，信息，假新闻和其他媒体的传播是至关重要的。在本文中，我们将依赖于同质网络属性的Keating等人在2022年开发的多类分支过程方法扩展到了更一般的聚类网络类别。使用社会启发的复杂传播模型，我们获得了结果，不仅是为了级联的平均行为，而且是用于级联特性的完整分布。我们引入了一种新方法，用于逆转概率生成函数以恢复其潜在的概率分布；该派生自然扩展到更高的维度。这种反演技术与多类分支过程一起使用，以获得级联属性的单变量和双变量分布。最后，使用集团覆盖方法，我们将方法应用于合成和现实世界网络，并将级联大小的理论分布与广泛的数值模拟结果进行比较。
Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this paper, we extend the multi-type branching process method developed in Keating et al., 2022, which relies on homogenous network properties, to a more general class of clustered networks. Using a model of socially-inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.
