Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Estimation of the Shortest and Largest Average Path Length in Graphs
  of Given Density   Many real world networks (graphs) are observed to be 'small worlds', i.e.,
the average path length among nodes is small. On the other hand, it is somewhat
unclear what other average path length values networks can produce. In
particular, it is not known what the maximum and the minimum average path
length values are. In this paper we provide a lower estimation for the shortest
average path length (l) values in connected networks, and the largest possible
average path length values in networks with given size and density. To the
latter end, we construct a special family of graphs and calculate their average
path lengths. We also demonstrate the correctness of our estimation by
simulations.

28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
18
The categories of this paper are: econ
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph