Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher order clustering coefficients in Barabasi-Albert networks   Higher order clustering coefficients $C(x)$ are introduced for random
networks. The coefficients express probabilities that the shortest distance
between any two nearest neighbours of a certain vertex $i$ equals $x$, when one
neglects all paths crossing the node $i$. Using $C(x)$ we found that in the
Barab\'{a}si-Albert (BA) model the average shortest path length in a node's
neighbourhood is smaller than the equivalent quantity of the whole network and
the remainder depends only on the network parameter $m$. Our results show that
small values of the standard clustering coefficient in large BA networks are
due to random character of the nearest neighbourhood of vertices in such
networks.

27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph