The Emergence of Benford's Distribution in Directed Networks: A Study of a Multiplicative Evolution Mechanism

Network degree distributions represent a fundamental topological characteristic of complex networks, yet the study of Benford's law in network generation models remains insufficiently explored. This paper introduces a novel Multiplicative Iterative Evolution (MIE) model that drives network evolution through iterative random multiplicative updates and topological reconnections on a fixed-size network. Simulation experiments demonstrate that the in-degree distributions of networks generated by this model converge stably and exhibit high conformity to Benford's law. The MIE model provides a new, non-growth generation paradigm for network science and offers a powerful generative mechanism for explaining potential Benford phenomena in real-world networks. Unlike traditional preferential attachment models that rely on network growth, our approach demonstrates that multiplicative processes alone can produce scale-invariant degree distributions following Benford's law through evolutionary dynamics on fixed network topologies. The model's robustness across parameter ranges and its theoretical grounding in log-uniform distributions establish it as a fundamental contribution to understanding the emergence of power-law-like phenomena in complex systems.