Diagonal Degree Correlations vs. Epidemic Threshold in Scale-Free Networks. (8th October 2021)

• Record Type: Journal Article
• Authors: Bertotti, M. L.; Modanese, G.
• Other Names: Zhu Xuzhen Academic Editor.
• Is Part Of: Complexity. Volume 2021(2021)
• Publication Date: 2021-10-08
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2021/7704586
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : We prove that the presence of a diagonal assortative degree correlation, even if small, has the effect of dramatically lowering the epidemic threshold of large scale-free networks. The correlation matrix considered is P h | k = 1 − r P h k U + r δ h k, where P U is uncorrelated and r (the Newman assortativity coefficient) can be very small. The effect is uniform in the scale exponent γ if the network size is measured by the largest degree n . We also prove that it is possible to construct, via the Porto–Weber method, correlation matrices which have the same k n n as the P h | k above, but very different elements and spectra, and thus lead to different epidemic diffusion and threshold. Moreover, we study a subset of the admissible transformations of the form P h | k ⟶ P h | k + Φ h, k with Φ h, k depending on a parameter which leaves k n n invariant. Such transformations affect in general the epidemic threshold. We find, however, that this does not happen when they act between networks with constant k n n, i.e., networks in which the average neighbor degree is independent from the degree itself (a wider class than that of strictly uncorrelated networks).