Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local rewiring algorithms to increase clustering and grow a small world   Many real-world networks have high clustering among vertices: vertices that
share neighbors are often also directly connected to each other. A network's
clustering can be a useful indicator of its connectedness and community
structure. Algorithms for generating networks with high clustering have been
developed, but typically rely on adding or removing edges and nodes, sometimes
from a completely empty network. Here, we introduce algorithms that create a
highly clustered network by starting with an existing network and rearranging
edges, without adding or removing them; these algorithms can preserve other
network properties even as the clustering increases. They rely on local
rewiring rules, in which a single edge changes one of its vertices in a way
that is guaranteed to increase clustering. This greedy step can be applied
iteratively to transform a random network into a form with much higher
clustering. Additionally, the algorithms presented grow a network's clustering
faster than they increase its path length, meaning that network enters a regime
of comparatively high clustering and low path length: a small world. These
algorithms may be a basis for how real-world networks rearrange themselves
organically to achieve or maintain high clustering and small-world structure.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph