论文标题
关于高阶网络影响框架之间的等效性：通用阈值，超图触发和逻辑触发模型
On the Equivalence Between High-Order Network-Influence Frameworks: General-Threshold, Hypergraph-Triggering, and Logic-Triggering Models
论文作者
论文摘要
在本文中，我们研究了几个高阶网络 - 侵入性 - 突出框架及其与经典网络扩散框架（例如触发模型和一般阈值模型）的联系。在一个框架中，我们使用Hyperedges代表多一对一的影响 - 一组节点对另一个节点的集体影响 - 并将HyperGraph触发模型定义为对经典触发模型的自然扩展。在另一个框架中，我们使用单调布尔函数来捕获多一对影响行为的不同逻辑，并将触发模型扩展到布尔函数触发模型。我们证明，布尔功能触发模型即使具有精致的影响力逻辑细节，也等同于HyperGraph触发模型，并且两者都等同于一般阈值模型。此外，在所有具有相同表达能力的模型中，一般阈值模型在参数数量上都是最佳的。我们通过在影响不同节点的影响传播之间引入相关性，进一步扩展了这三个等效模型。令人惊讶的是，我们发现，基于相关的超图模型仍然等同于相关的基于布尔函数的模型，但相关的一般阈值模型比两个高级模型更具限制性。我们的研究通过提供对现有模型中的群体影响行为的新见解，以及了解影响网络传播的多种建模工具，从而阐明了高阶网络影响传播。
In this paper, we study several high-order network-influence-propagation frameworks and their connection to the classical network diffusion frameworks such as the triggering model and the general threshold model. In one framework, we use hyperedges to represent many-to-one influence -- the collective influence of a group of nodes on another node -- and define the hypergraph triggering model as a natural extension to the classical triggering model. In another framework, we use monotone Boolean functions to capture the diverse logic underlying many-to-one influence behaviors, and extend the triggering model to the Boolean-function triggering model. We prove that the Boolean-function triggering model, even with refined details of influence logic, is equivalent to the hypergraph triggering model, and both are equivalent to the general threshold model. Moreover, the general threshold model is optimal in the number of parameters, among all models with the same expressive power. We further extend these three equivalent models by introducing correlations among influence propagations on different nodes. Surprisingly, we discover that while the correlated hypergraph-based model is still equivalent to the correlated Boolean-function-based model, the correlated general threshold model is more restrictive than the two high-order models. Our study sheds light on high-order network-influence propagations by providing new insight into the group influence behaviors in existing models, as well as diverse modeling tools for understanding influence propagations in networks.
