Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Funnelling effect in networks   Funnelling effect, in the context of searching on networks, precisely
indicates that the search takes place through a few specific nodes. We define
the funnelling capacity $f$ of a node as the fraction of successful dynamic
paths through it with a fixed target. The distribution $D(f)$ of the fraction
of nodes with funnelling capacity $f$ shows a power law behaviour in random
networks (with power law or stretched exponential degree distribution) for a
considerable range of values of the parameters defining the networks.
Specifically we study in detail $D_1=D(f=1)$, which is the quantity signifying
the presence of nodes through which all the dynamical paths pass through. In
scale free networks with degree distribution $P(k) \propto k^{-\gamma}$, $D_1$
increases linearly with $\gamma$ initially and then attains a constant value.
It shows a power law behaviour, $D_1 \propto N^{-\rho}$, with the number of
nodes $N$ where $\rho$ is weakly dependent on $\gamma$ for $\gamma > 2.2$. The
latter variation is also independent of the number of searches. On stretched
exponential networks with $P(k) \propto \exp{(-k^\delta)}$, $\rho$ is strongly
dependent on $\delta$. The funnelling distribution for a model social network,
where the question of funnelling is most relevant, is also investigated.

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The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex