Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The strong giant in a random digraph   Consider a random directed graph on $n$ vertices with independent identically
distributed outdegrees with distribution $F$ having mean $\mu$, and
destinations of arcs selected uniformly at random. We show that if $\mu >1$
then for large $n$ there is very likely to be a unique giant strong component
with proportionate size given as the product of two branching process survival
probabilities, one with offspring distribution $F$ and the other with Poisson
offspring distribution with mean $\mu$. If $\mu \leq 1$ there is very likely to
be no giant strong component. We also extend this to allow for $F$ varying with
$n$.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: cs
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org