Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal Intervals of Decrease and Inflection Points for Node Reliability   The \textit{node reliability} of a graph $G$ is the probability that at least
one node is operational and that the operational nodes can all communicate in
the subgraph that they induce, given that the edges are perfectly reliable but
each node operates independently with probability $p\in[0,1]$. We show that
unlike many other notions of graph reliability, the number of maximal intervals
of decrease in $[0,1]$ is unbounded, and that there can be arbitrarily many
inflection points in the interval as well.

0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio