The Evolution of Ego-Centric Triads: A Microscopic Approach toward Predicting Macroscopic Network Properties

Scalability issues make it time-consuming to estimate even simple characteristics of large scale, online networks, and the constantly evolving qualities of these networks make it challenging to capture a representative picture of a particular network\´s properties. Here we focus on the evolution of all triads (ties between three nodes) in a graph, as a method of studying changeover time in large scale, online social networks. For three month snapshots, we examine, and predict, transitions among all sixteen triad types (i.e., triad census) in a sample of three years of Facebook wall-post interactions. We introduce a new sampling approach for examining triads in online graphs, based on ego-centric networks of random seeds. We examine tendencies in the data toward properties related to balance theory, including structural balance, cluster ability, ranked clusters, transitivity, hierarchical clusters, and the presence of "forbidden" triads. In a time series analysis, we successfully predict the evolution over time in the wall post network dataset, with relatively low levels of error. The findings demonstrate the utility of our ego-centric, two-step, random seed sampling approach for studying large scale networks and predicting macroscopic graph properties, as well as the advantages of examining transitions in the complete triad census for an online network.