Pyramid as a Core Structure in Social Networks

The significance of pyramid structures in dominating social networks is often mentioned, but the concept lacks a precise definition and comprehensive empirical analysis. To fill this gap, this paper offers a rigorous definition of pyramid structure, characterizing it as an expanding rooted tree. Empirical evidence, drawn from an extensive study of real-world social networks, corroborates existing hypotheses about the prevalence of large pyramid structures in such networks. Additionally, we identify a unique network characteristic: pyramid sizes vary across different types of networks. This finding suggests that existing models may not be sufficient for accurately representing real-world social networks and calls for the development of a new model. The paper also explores more characteristics and applications of pyramid in developing network metrics and structures, touching on aspects like degree distribution, clustering coefficient, core-periphery structures, and small-world networks.