Modelling the growth of the network value

We investigate the evolution of network effects, specifically focusing on the emerging paradigm of third-generation networks known as group-forming networks (GFNs). In contrast to traditional views where network value adheres to Metcalfe's quadratic growth or Sarnoff's linear growth, GFNs, such as social networks and community-centric platforms like Apple, Microsoft, and Google, exhibit a distinct exponential growth pattern in network value as postulated by Reed's hypothesis. Unlike conventional network science, economic perspectives on network effects do not necessitate precise knowledge of the network topology. Instead, they often align with mean-field models akin to those found in statistical physics. Recent empirical studies challenge earlier assumptions, revealing that many GFNs have undergone exponential or notably superquadratic growth, deviating significantly from established models based solely on user and link counts. This paper introduces a simplified model aimed at capturing the growth dynamics of marketable groups within a network comprising n users. The model explores various hypothetical mechanisms governing the expansion of these groups, and through rigorous analysis and simulation, we uncover compelling evidence that the observed growth in GFNs surpasses traditional quadratic models. Our findings challenge existing notions, suggesting a new framework for understanding the intricacies of network growth dynamics, and providing solid analytical and conceptual foundations for the recent explosive processes of economic and financial value growth of networks that exploit the formation of groups.