Quantifying the Dynamics of Network Detachment Across Scientific, Technological, Commercial, and Pharmacological Domains.

Despite the vast literature on complex network dynamics, our understanding of the network detachment process remains limited. This understanding is essential for deeper insight into network evolution. Here, we analyze four large-scale datasets that capture the structural patterns of detachment across scientific, technological, commercial, and pharmacological domains. Across these diverse domains, we uncover one simple pattern of preferential detachment in social systems, whereby the probability for individuals or organizations to disengage from a previously adopted practice correlates with the number of network neighbors who have already detached. To examine the structural consequences of this empirical pattern, we show that preferential detachment can fundamentally alter how networked systems disintegrate, inducing a phase transition in systems typically considered robust against detachment. We further derive an analytical framework to systematically understand the impact of preferential detachment on network dynamics, pinpointing the topological conditions under which it accelerates, decelerates, or leaves unchanged the breakdown of the network compared with random detachment. Together, these results demonstrate that the detachment dynamics follow simple yet reproducible patterns, deepening our quantitative understanding of detachment within networked social systems, with implications for the robustness and functioning of innovation communities.