Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local structure of directed networks   Previous work on undirected small-world networks established the paradigm
that locally structured networks tend to have high density of short loops. On
the other hand, many realistic networks are directed. Here we investigate the
local organization of directed networks and find, surprisingly, that real
networks often have very few short loops as compared to random models. We
develop a theory and derive conditions for determining if a given network has
more or less loops than its randomized counterpart. These findings carry broad
implications for structural and dynamical processes sustained by directed
networks.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph