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An extremal problem: How small scale-free graph can be | | Fei Ma
; Ping Wang
; Bing Yao
; | | Date: |
21 Nov 2019 | | Abstract: | The bloom of complex network study, in particular, with respect to scale-free
ones, is considerably triggering the research of scale-free graph itself.
Therefore, a great number of interesting results have been reported in the
past, including bounds of diameter. In this paper, we focus mainly on a problem
of how to analytically estimate the lower bound of diameter of scale-free
graph, i.e., how small scale-free graph can be. Unlike some pre-existing
methods for determining the lower bound of diameter, we make use of a
constructive manner in which one candidate model $mathcal{G^*} (mathcal{V^*},
mathcal{E^*})$ with ultra-small diameter can be generated. In addition, with a
rigorous proof, we certainly demonstrate that the diameter of graph
$mathcal{G^{*}}(mathcal{V^{*}},mathcal{E^{*}})$ must be the smallest in
comparison with that of any scale-free graph. This should be regarded as the
tight lower bound. | | Source: | arXiv, 1911.9253 | | Services: | Forum | Review | PDF | Favorites | |
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