  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.
