Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reappraising the distribution of the number of edge crossings of graphs
  on a sphere   Many real transportation and mobility networks have their vertices placed on
the surface of the Earth. In such embeddings, the edges laid on that surface
may cross. In his pioneering research, Moon analyzed the distribution of the
number of crossings on complete graphs and complete bipartite graphs whose
vertices are located uniformly at random on the surface of a sphere assuming
that vertex placements are independent from each other. Here we revise his
derivation of that variance in the light of recent theoretical developments on
the variance of crossings and computer simulations. We show that Moon's
formulae are inaccurate in predicting the true variance and provide exact
formulae.

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg