Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Percolation and Epidemic Processes in One-Dimensional Small-World
  Networks   We obtain tight thresholds for bond percolation on one-dimensional
small-world graphs, and apply such results to obtain tight thresholds for the
\emph{Independent Cascade} process and the \emph{Reed-Frost} process in such
graphs. These are the first fully rigorous results establishing a phase
transition for bond percolation and SIR epidemic processes in small-world
graphs. Although one-dimensional small-world graphs are an idealized and
unrealistic network model, a number of realistic qualitative epidemiological
phenomena emerge from our analysis, including the epidemic spread through a
sequence of local outbreaks, the danger posed by random connections, and the
effect of super-spreader events.

9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess