Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust subgraph counting with distribution-free random graph analysis   Subgraphs such as cliques, loops and stars form crucial connections in the
topologies of real-world networks. Random graph models provide estimates for
how often certain subgraphs appear, which in turn can be tested against
real-world networks. These subgraph counts, however, crucially depend on the
assumed degree distribution. Fitting a degree distribution to network data is
challenging, in particular for scale-free networks with power-law degrees. In
this paper we develop robust subgraph counts that do not depend on the entire
degree distribution, but only on the mean and mean absolute deviation (MAD),
summary statistics that are easy to obtain for most real-world networks. By
solving an optimization problem, we provide tight (the sharpest possible)
bounds for the subgraph counts, for all possible subgraphs, and for all
networks with degree distributions that share the same mean and MAD. We
identify the extremal random graph that attains the tight bounds as the graph
with a specific three-point degree distribution. We leverage the bounds to
obtain robust scaling laws for how the numbers of subgraphs grow as function of
the network size. The scaling laws indicate that sparse power-law networks are
not the most extreme networks in terms of subgraph counts, but dense power-law
networks are. The robust bounds are also shown to hold for several real-world
data sets.

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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn