Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplexity versus correlation: the role of local constraints in real
  multiplexes   Several real-world systems can be represented as multi-layer complex
networks, i.e. in terms of a superposition of various graphs, each related to a
different mode of connection between nodes. Hence, the definition of proper
mathematical quantities aiming at capturing the level of complexity of those
systems is required. Various attempts have been made to measure the empirical
dependencies between the layers of a multiplex, for both binary and weighted
networks. In the simplest case, such dependencies are measured via
correlation-based metrics: we show that this is equivalent to the use of
completely homogeneous benchmarks specifying only global constraints, such as
the total number of links in each layer. However, these approaches do not take
into account the heterogeneity in the degree and strength distributions, which
are instead a fundamental feature of real-world multiplexes. In this work, we
compare the observed dependencies between layers with the expected values
obtained from reference models that appropriately control for the observed
heterogeneity in the degree and strength distributions. This leads to novel
multiplexity measures that we test on different datasets, i.e. the
International Trade Network (ITN) and the European Airport Network (EAN). Our
findings confirm that the use of homogeneous benchmarks can lead to misleading
results, and furthermore highlight the important role played by the
distribution of hubs across layers.

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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: math
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin