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.

翻译：我们研究了一种基于图模型的Galam观点形成模型泛化。考虑一个代表社交网络的简单连通图，图中每个节点被染成蓝色或白色，分别表示对新产品或话题的正面或负面观点。在每个离散时间轮次中，所有节点被随机分配到不同规模的组中，其中每组节点构成底层图上的一个团。所有节点同时将其颜色更新为所在组的多数颜色。若出现平局，则组内每个节点以均匀随机概率从两种颜色中任意选择一种。通过研究该模型的收敛时间，实验表明：完全图的收敛时间是节点数量的对数函数，而环形图的收敛时间则是二次函数。受病毒式营销启发，我们还研究了多种策略来选择种子节点集合，以最大化两种颜色之一的最终级联效应。我们考虑基于图结构（节点的中心性指标，如度、介数、接近中心性）和个体特征（活跃度与固执度）选择种子节点的算法，并通过在不同真实网络与合成网络上进行实验，比较了这些策略的效果。