Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling properties of first-passage quantities on the fractal and
  transfractal scale free networks   In this paper, we consider the random walk process on a kind of fractal (or
transfractal) scale free networks, which also called as $(u,v)$ flowers, and we
focus on the global first passage time (GFPT) and first return time (FRT).
Here, we present method to derive exactly the probability generation function,
mean and variance of the GFPT and FRT for a given hub (i.e., node with the
highest degree) and then the scaling properties of the mean and the variance of
the GFPT and FRT are disclosed. Our results show that, for the case of $u>1$,
while the networks are fractals, the mean of the GFPT scales with the volume of
the network as $\langle GMFPT_t\rangle \sim N_t^{{2}/{d_s}}$, where $\langle *
\rangle$ denotes the mean of random variable $*$, $N_t$ is the volume of the
network with generation $t$ and $d_s$ is the spectral dimension of the network;
but, for the case of $u=1$, while the networks are nonfractals, the mean of the
GFPT scales as $\langle GMFPT_t\rangle \sim N_t^{{2}/{\tilde{d}_s}}$, where
$\tilde{d}_s$ is the transspectral dimension of the network, which is
introduced in this paper. Results also show that, the variance of the GFPT
scales as $Var(GFPT_t) \sim \langle GFPT_{t}\rangle^2$, where $Var(*)$ denotes
variance of of random variable $*$; whereas the variance of the FRT scales as
$Var(FRT_t) \sim \langle FRT_{t} \rangle \langle GFPT_{t}\rangle$.
%$Var(GFPT_t) \sim \langle GFPT_{t}\rangle^2$ and $Var(FRT_t) \sim \langle
FRT_{t} \rangle \langle GFPT_{t}\rangle$, where $Var(GFPT_t)$ and $Var(FRT_t)$
denote the variance of the GFPT and the FRT, $\langle GFPT_{t}\rangle$ and
$\langle FRT_{t}\rangle$ denote the mean of the GFPT and the FRT respectively.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an