Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All scale-free networks are sparse   We study the realizability of scale free-networks with a given degree
sequence, showing that the fraction of realizable sequences undergoes two
first-order transitions at the values 0 and 2 of the power-law exponent. We
substantiate this finding by analytical reasoning and by a numerical method,
proposed here, based on extreme value arguments, which can be applied to any
given degree distribution. Our results reveal a fundamental reason why large
scale-free networks without constraints on minimum and maximum degree must be
sparse.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph