基于图的伽蓝模型泛化:收敛时间和影响节点

Physics Pub Date : 2023-11-28 DOI:10.3390/physics5040071
Sining Li, Ahad N. Zehmakan
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引用次数: 0

摘要

我们研究的是基于图的伽拉姆舆论形成模型的一般化。考虑一个代表社交网络的简单连接图。图中的每个节点都被染成蓝色或白色,表示对新产品或话题的积极或消极看法。在每一轮离散时间中,所有节点被随机分配到不同大小的组中,每个组中的节点在底层图中形成一个小群。所有节点同时更新自己的颜色,使之成为本组中的多数颜色。如果出现平局,则组中的每个节点统一随机选择两种颜色中的一种。我们对模型的收敛时间进行了研究,实验表明,对于完整图,收敛时间是节点数的对数函数,而对于循环图,收敛时间是二次函数。受病毒式营销的启发,我们还研究了选择一组种子节点以最大化两种颜色之一的最终级联的各种策略。我们考虑了根据图结构(节点的中心度量,如度、间隔度和接近度)和个体特征(活跃性和固执性)选择种子节点的算法。我们通过在不同的真实世界和合成网络上进行实验,对这些策略进行了比较。
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Graph-Based Generalization of Galam Model: Convergence Time and Influential Nodes
We study a graph-based generalization of the Galam opinion formation model. Consider a simple connected graph which represents a social network. Each node in the graph is colored either blue or white, which indicates a positive or negative opinion on a new product or a topic. In each discrete-time round, all nodes are assigned randomly to groups of different sizes, where the node(s) in each group form a clique in the underlying graph. All the nodes simultaneously update their color to the majority color in their group. If there is a tie, each node in the group chooses one of the two colors uniformly at random. Investigating the convergence time of the model, our experiments show that the convergence time is a logarithm function of the number of nodes for a complete graph and a quadratic function for a cycle graph. We also study the various strategies for selecting a set of seed nodes to maximize the final cascade of one of the two colors, motivated by viral marketing. We consider the algorithms where the seed nodes are selected based on the graph structure (nodes’ centrality measures such as degree, betweenness, and closeness) and the individual’s characteristics (activeness and stubbornness). We provide a comparison of such strategies by conducting experiments on different real-world and synthetic networks.
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