Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale-free network clustering in hyperbolic and other random graphs   Random graphs with power-law degrees can model scale-free networks as sparse
topologies with strong degree heterogeneity. Mathematical analysis of such
random graphs proved successful in explaining scale-free network properties
such as resilience, navigability and small distances. We introduce a
variational principle to explain how vertices tend to cluster in triangles as a
function of their degrees. We apply the variational principle to the hyperbolic
model that quickly gains popularity as a model for scale-free networks with
latent geometries and clustering. We show that clustering in the hyperbolic
model is non-vanishing and self-averaging, so that a single random graph sample
is a good representation in the large-network limit. We also demonstrate the
variational principle for some classical random graphs including the
preferential attachment model and the configuration model.

32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph