Growth-induced percolation on complex networks.

Empirical studies have increasingly highlighted the crucial role of indirect social interactions in shaping human behaviors, yet theoretical models have largely focused on direct influences. By analyzing scientific collaboration networks, we demonstrate that direct and indirect collaborators are key in triggering high-impact research periods. Inspired by these findings, we propose a novel model, growth-induced percolation, which captures how individuals are activated through indirect interactions. Our model reveals a striking asymmetry in the hysteresis loop between growth-induced percolation and its reverse process, with distinct phase transition behaviors. Our work provides a foundational framework for understanding how indirect interactions drive the spread of behaviors in social systems, with implications for fields ranging from scientific collaboration to social contagion.