Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection timeopen access
- Authors
- Lee, Mi Jin; Lee, Deok-Sun
- Issue Date
- Mar-2019
- Publisher
- AMER PHYSICAL SOC
- Citation
- Physical Review E, v.99, no.3, pp.1 - 9
- Indexed
- SCIE
SCOPUS
- Journal Title
- Physical Review E
- Volume
- 99
- Number
- 3
- Start Page
- 1
- End Page
- 9
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/3403
- DOI
- 10.1103/PhysRevE.99.032309
- ISSN
- 2470-0045
- Abstract
- For a reliable prediction of an epidemic or information spreading pattern in complex systems, well-defined measures are essential. In the susceptible-infected model on heterogeneous networks, the cluster of infected nodes in the intermediate-time regime exhibits too large fluctuation in size to use its mean size as a representative value. The cluster size follows quite a broad distribution, which is shown to be derived from the variation of the cluster size with the time when a hub node was first infected. On the contrary, the distribution of the time taken to infect a given number of nodes is well concentrated at its mean, suggesting the mean infection time is a better measure. We show that the mean infection time can be evaluated by using the scaling behaviors of the boundary area of the infected cluster and use it to find a nonexponential but algebraic spreading phase in the intermediate stage on strongly heterogeneous networks. Such slow spreading originates in only small-degree nodes left susceptible, while most hub nodes are already infected in the early exponential-spreading stage. Our results offer a way to detour around large statistical fluctuations and quantify reliably the temporal pattern of spread under structural heterogeneity.
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