Research on Optimization Model of Scale-Free Networks with Agent Exit Effects Based on Interval Numbers

In the real world, agent exit behaviors, characterized by their diversity and uncertainty, significantly impact the evolution of networks, and in extreme cases, can even lead to network degradation. To reasonably quantify the uncertainty associated with agent exits, this study employs interval number methods and integrates three typical agent exit modes to construct an optimization model of scale-free networks with agent exit effects based on interval numbers. This model aims to analyze the impact of agent exits on network heterogeneity and small-world characteristics. The research results indicate that when the number of agent exits does not exceed the number of entries, as the network continues to evolve, the influence of agent exit modes on network structure gradually diminishes, and the network degree distribution exhibits power-law characteristics. Furthermore, under scenarios with predetermined agent exit modes and longer evolution times, there is a significant negative correlation between network heterogeneity and small-world characteristics and the uncertainty associated with agent exits.