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：我们研究了基于图的Galam意见形成模型的泛化版本。考虑一个表示社交网络的简单连通图。图中每个节点被标记为蓝色或白色，分别表示对新产品或话题的正面或负面意见。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群组中，其中每个群组内的节点在底层图中构成一个团。所有节点同时将其颜色更新为所在群组的多数颜色。若出现平局，群组中的每个节点以均匀概率随机选择两种颜色之一。通过探究模型的收敛时间，实验表明：在完全图上收敛时间为节点数的对数函数，而在环图上为二次函数。受病毒式营销启发，我们还研究了多种种子节点选择策略，以最大化两种颜色中某一颜色的最终级联规模。我们考虑了基于图结构（节点的度、介数、紧密度等中心性度量）和个体特征（活跃度与固执度）选择种子节点的算法，并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。