Hierarchical centralities of information transmissions in reaching a consensus

Abstract

The question, how central indications arise from an undirected environment and lead to collective behaviors, is analyzed based on a simple model of opinion dynamics, called the DeGroot model. We first reformulate the necessary and sufficient condition for reaching a consensus, then the condition is used to set up the pattern of information transmissions. By classifying the individuals into a sequential series of classes and by giving the dynamic contents of centrality, we demonstrate that the hierarchical centralities with descend strength are associated with the sequential series of classes in information transmissions. The results provide wide applications in social engineering, an example about the merger of different groups is discussed.