Network evolution of centrality maximizing agents: An empirical evidence of nestedness emergence.

In this study, we investigate the relationship between agents' efforts to maximize their centrality and the emergence of nested structures in networks. Using the Bitcoin Lightning Network (BLN) as a unique dataset, we analyze its dynamic evolution through the nested overlap and decreasing fill method, modularity analysis, an in-block nestedness model, and randomized null models. Our findings reveal a substantial increase in nested and in-block nested structures as the BLN expands, driven by nodes' strategic behavior to enhance their importance. To validate these results, we develop a two-stage game-theoretic model incorporating novel parameters such as the social distance factor and social reduction factor. This model generates stochastically stable networks that replicate the observed structures. Maximum likelihood estimation confirms the model's ability to reproduce the nested patterns seen in the BLN, particularly at larger scales, underscoring its broader applicability to other complex systems. This work advances the understanding of how microlevel strategies, such as centrality maximization, drive the emergence of macrolevel structural properties like nestedness. The results have significant implications for the study of network dynamics, resilience, and optimization, providing a foundation for further exploration in networks with similar characteristics.