Endemic infections are always possible on regular networks

Abstract

We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behaviour via an analytical approach based on the network structure, and provide an exact equation describing the numerical results. Our work indicates that intrinsic structural properties always allow the spread of epidemics on regular networks.

5 pages, 4 figures

References in corpus (13)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Epidemic spreading in scale-free networks
• Random graphs with clustering
• Networks and the Epidemiology of Infectious Disease
• Percolation and Epidemic Thresholds in Clustered Networks
• Efficient and exact sampling of simple graphs with given arbitrary degree sequence
• All scale-free networks are sparse
• Random Networks with Tunable Degree Distribution and Clustering
• Constructing and sampling directed graphs with given degree sequences
• Sparse random graphs with clustering
• Analytical results for bond percolation and k-core sizes on clustered networks
• Chaos in a spatial epidemic model

Cited by in corpus (8)

• Synchronization in networks with multiple interaction layers
• Degree correlations in directed scale-free networks
• Exact sampling of graphs with prescribed degree correlations
• Fast and accurate determination of modularity and its effect size
• Finding network communities using modularity density
• Dynamic Behavior of Interacting between Epidemics and Cascades on Heterogeneous Networks
• Relaxation dynamics of maximally clustered networks
• Consistent Approximation of Epidemic Dynamics on Degree-heterogeneous Clustered Networks