Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The average number of distinct sites visited by a random walker on
  random graphs   We study the linear large $n$ behavior of the average number of distinct
sites $S(n)$ visited by a random walker after $n$ steps on a large random
graph. An expression for the graph topology dependent prefactor $B$ in $S(n) =
Bn$ is proposed. We use generating function techniques to relate this prefactor
to the graph adjacency matrix and then devise message-passing equations to
calculate its value. Numerical simulations are performed to evaluate the
agreement between the message passing predictions and random walk simulations
on random graphs. Scaling with system size and average graph connectivity are
also analysed.

2
The categories of this paper are: math
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph