Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counterexample: scale-free networked graphs with invariable diameter and
  density feature   Here, we propose a class of scale-free networks $G(t;m)$ 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 $\langle k\rangle$ of all the generated networks 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 networks 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
networks 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 networks $G(t;m)$ and then
obtain closed-form solution to mean hitting time $\langle
\mathcal{H}\rangle_{t}$. As opposed to other previous models, our results show
an unexpected phenomenon that the analytic value for $\langle
\mathcal{H}\rangle_{t}$ is approximately close to the logarithm of vertex
number of networks $G(t;m)$. From the theoretical point of view, these
networked models considered here can be thought of as counterexamples for most
of the published models obeying power-law distribution in current study.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con