Robustness of regular ring lattices based on natural connectivity |
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| Authors: | J. Wu M. Barahona Y.-J. Tan H.-Z. Deng |
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| Affiliation: | 1. Department of Management , College of Information Systems and Management, National University of Defence Technology , Changsha 410073, P.R. China;2. Institute for Mathematical Sciences, Imperial College London , London SW7 2PG, UK wujunpla@hotmail.com;4. Institute for Mathematical Sciences, Imperial College London , London SW7 2PG, UK;5. Department of Bioengineering , Imperial College London , London SW7 2AZ, UK;6. Department of Management , College of Information Systems and Management, National University of Defence Technology , Changsha 410073, P.R. China |
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| Abstract: | It has been recently proposed that natural connectivity can be used to efficiently characterise the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating the weighted number of closed walks of all lengths and can be seen as an average eigenvalue obtained from the graph spectrum. In this article, we explore both analytically and numerically the natural connectivity of regular ring lattices and regular random graphs obtained through degree-preserving random rewirings from regular ring lattices. We reformulate the natural connectivity of regular ring lattices in terms of generalised Bessel functions and show that the natural connectivity of regular ring lattices is independent of network size and increases with K monotonically. We also show that random regular graphs have lower natural connectivity, and are thus less robust, than regular ring lattices. |
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| Keywords: | natural connectivity robustness regular ring lattices random regular graphs generalised Bessel function |
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