Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structural properties of small-world networks with finite range
  of shortcut links   We explore a new variant of Small-World Networks (SWNs), in which an
additional parameter ($r$) sets the length scale over which shortcuts are
uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$
corresponds to the original SWN model. These short-range SWNs have a similar
degree distribution and scaling properties as the original SWN model. We
observe the small-world phenomenon for $r \ll 1$ indicating that global
shortcuts are not necessary for the small-world effect. For short-range SWNs,
the average path length changes nonmonotonically with system size, whereas for
the original SWN model it increases monotonically. We propose an expression for
the average path length for short-range SWNs based on numerical simulations and
analytical approximations.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph