Intersection of random spanning trees in complex networks

Abstract

Abstract In their previous work, the authors considered the concept of random spanning tree intersection of complex networks (London and Pluhár, in: Cherifi, Mantegna, Rocha, Cherifi, Micciche (eds) Complex networks and their applications XI, Springer, Cham, 2023). A simple formula was derived for the size of the minimum expected intersection of two spanning trees chosen uniformly at random. Monte Carlo experiments were run for real networks. In this paper, we provide a broader context and motivations for the concept, discussing its game theoretic origins, examples, its applications to network optimization problems, and its potential use in quantifying the resilience and modular structure of complex networks.

Keywords

• Random spanning trees
• Small-world networks
• Modularity
• Network resilience
• Spanning tree game