Network Evolution Through Directed Triadic Closure

Abstract

This research aims to design a directed social network by utilizing the principle of directed triadic closure. Two points of view were taken into account to investigate the network dynamics. One is at the microscopic level, which tracks the precise changes in the network’s structure. The other level is the macroscopic level. This model considers counting the edges in the social network at each time t, which gives the general picture of the structure of the proposed social network. Through this work, we derive a rigorous analysis of the cubic polynomial that depicts the network evolution of the undirected model proposed by Giovacchino, Higham, and Zygalakis [1]. In addition, we derive another analysis for the quartic polynomial that describes the edge density of our directed social network. Both the analysis of the cubic and quartic polynomials provide insights into which suitable constant rates c1, c2 and c3 for birth, death, and triadic closure between nodes within the social network in the undirected and newly proposed directed models, respectively. The results reveal the high sensitivity of the dynamical system to the small variations in the parameter rates. In addition, other computational analyses were conducted to investigate the two proposed models, the micro and macro models. At the end of the dissertation, we provide recommendations based on our results, as well as suggestions for future studies worth investigating.