Periodic boundary condition effects in small-world networks

Abstract

Understanding boundary conditions is crucial for properly modeling interactions and constraints within a system. In particular, periodic boundary conditions play an important role, because they allow systems to be treated as if existing in a continuous, constraint-free space, with significant relevance across diverse scientific fields. Our study explores the effects of periodic boundary conditions on Small-World networks by comparing traditional and flat versions derived from Ring and Line networks, respectively, through comparisons of network metrics and disconnection assessments. Recognizing the critical role of network topology in the behavior of dynamical models, we use an epidemic model to show that the structure of a network can either facilitate or hinder the spread of disease, emphasizing the importance of boundary conditions on these dynamics. The faster spread of disease in Ring networks, with shorter Average Shortest Paths, as well as their resilience on keeping network connectivity under rewiring, illustrate the impact that periodic boundary conditions can have on epidemic scenarios.