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Article overview
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Counterexample: scale-free networked graphs with invariable diameter and density feature | | Fei Ma
; Xiaomin Wang
; Ping Wang
; | | Date: |
2 Dec 2019 | | Abstract: | Here, we propose a class of scale-free networked graphs $G(t;m)$ with some
intriguing properties, which can not be simultaneously held by all the
theoretical models with power-law degree distribution in the existing
literature, including (i) average degrees $langle k
angle$ of all the
generated graphs are no longer a constant in the limit of large graph size,
implying that they are not sparse but dense, (ii) power-law parameters $gamma$
of these models are precisely calculated equal to $2$, as well (iii) their
diameters $D$ are all an invariant in the growth process of models. While our
models have deterministic structure with clustering coefficients equivalent to
zero, we might be able to obtain various candidates with nonzero clustering
coefficient based on original graphs using some reasonable approaches, for
instance, randomly adding some new edges under the premise of keeping the three
important properties above unchanged. In addition, we study trapping problem on
graphs $G(t;m)$ and then obtain closed-form solutions $langle HT
angle_{t}$
to mean hitting time. As opposed to other models, our results show an
unexpected phenomenon that $langle HT
angle_{t}$ is approximately close to
the logarithm of order of graphs $G(t;m)$ however not to the order itself. From
the theoretical point of view, these networked graphs considered here can be
thought of as counterexamples for most of the published models obeying
power-law distribution in current study. | | Source: | arXiv, 2001.3525 | | Services: | Forum | Review | PDF | Favorites | |
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