Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-avoiding walks and connective constants in clustered scale-free
  networks   Various types of walks on complex networks have been used in recent years to
model search and navigation in several kinds of systems, with particular
emphasis on random walks. This gives valuable information on network
properties, but self-avoiding walks (SAWs) may be more suitable than
unrestricted random walks to study long-distance characteristics of complex
systems. Here we study SAWs in clustered scale-free networks, characterized by
a degree distribution of the form $P(k) \sim k^{-\gamma}$ for large $k$.
Clustering is introduced in these networks by inserting three-node loops
(triangles). The long-distance behavior of SAWs gives us information on
asymptotic characteristics of such networks. The number of self-avoiding walks,
$a_n$, has been obtained by direct enumeration, allowing us to determine the
{\em connective constant} $\mu$ of these networks as the large-$n$ limit of the
ratio $a_n / a_{n-1}$. An analytical approach is presented to account for the
results derived from walk enumeration, and both methods give results agreeing
with each other. In general, the average number of SAWs $a_n$ is larger for
clustered networks than for unclustered ones with the same degree distribution.
The asymptotic limit of the connective constant for large system size $N$
depends on the exponent $\gamma$ of the degree distribution: For $\gamma > 3$,
$\mu$ converges to a finite value as $N \to \infty$; for $\gamma = 3$, the
size-dependent $\mu_N$ diverges as $\ln N$, and for $\gamma < 3$ we have $\mu_N
\sim N^{(3 - \gamma) / 2}$.

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The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
23
The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol