Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neighbor selection and hitting probability in small-world graphs   Small-world graphs, which combine randomized and structured elements, are
seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this
type it is possible to route, or navigate, between vertices in few steps even
with very little knowledge of the graph itself. In an attempt to understand how
such graphs arise we introduce a different criterion for graphs to be navigable
in this sense, relating the neighbor selection of a vertex to the hitting
probability of routed walks. In several models starting from both discrete and
continuous settings, this can be shown to lead to graphs with the desired
properties. It also leads directly to an evolutionary model for the creation of
similar graphs by the stepwise rewiring of the edges, and we conjecture,
supported by simulations, that these too are navigable.

26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio