Endemic infections are always possible on regular networks

Area of Science:

• Network Science
• Epidemiology
• Statistical Physics

Background:

• Understanding the behavior of large-scale networks is crucial in various scientific domains.
• The interplay between network topology and emergent properties, such as component size, remains an active area of research.
• Epidemic spread dynamics are significantly influenced by the underlying network structure.

Purpose of the Study:

• To investigate the relationship between the largest connected component and the clustering coefficient in regular networks.
• To determine if a phase transition occurs in the size of the largest component as the clustering coefficient varies.
• To provide an analytical explanation for the observed behavior and its implications for epidemic spread.

Main Methods:

• Analytical modeling based on the intrinsic structure of regular networks.
• Numerical simulations to observe the behavior of the largest component.
• Derivation of an exact equation to describe the numerical findings.

Main Results:

• The size of the largest connected component in regular networks exhibits a smooth dependence on the clustering coefficient.
• No abrupt phase transition was observed in the component size.
• An exact analytical equation accurately describes the numerical results.

Conclusions:

• The clustering coefficient does not induce a phase transition in the largest component size of regular networks.
• The inherent structural properties of regular networks facilitate the continuous spread of epidemics.
• The findings offer a deeper understanding of network robustness and epidemic propagation.