Effect of Node Weight Distributions on Critical Percolation Behavior in Weighted Networks

Abstract

Percolation theory provides a fundamental framework for understanding connectivity transitions in complex networks. While previous studies have primarily focused on topological structures, the role of node weight distributions in shaping percolation behavior remains insufficiently explored. In this study, we systematically investigate how different node weight distributions affect critical percolation properties in weighted networks. Four representative distributions—uniform, normal, exponential, and power-law—are considered. Numerical simulations show that weight heterogeneity significantly influences both the percolation threshold and the size of the largest connected component at criticality. In particular, highly heterogeneous distributions lead to earlier phase transitions but may result in reduced connectivity at critical states. These findings highlight the importance of weight distribution characteristics in determining network robustness and provide insights for the design and analysis of real-world infrastructure systems.