Activity constraints and the emergence of non-scale-free networks: Evidence from hip-hop and academia

Power-law distributions are widely used to characterize complex networks, yet recent work shows that scale-freeness is far less universal than once assumed, especially in social networks. We propose activity constraints—the finite time and effort required to complete collaborative ties—as a mechanism that limits hub growth and produces non-scale-free degree distributions. Using synthetic models and mathematical derivations, we show that imposing capacity limits on high-quality actors shifts degree distributions away from power laws and toward log-normal forms. We then examine degree saturation in two empirical settings: hip-hop featuring networks and academic coauthorship networks. In both cases, high-quality actors receive more ties, but their realized degree saturates relative to expectations, yielding sublinear or S-shaped quality-degree relationships. These findings demonstrate how micro-level workload constraints generate macro-level deviations from scale-free structure and highlight the importance of distinguishing activity-intensive from low-cost tie-formation processes when evaluating claims of scale-freeness in networks.