Research Article
Funnelling Effect in Networks
@INPROCEEDINGS{10.1007/978-3-642-02469-6_49, author={Parongama Sen}, title={Funnelling Effect in Networks}, proceedings={Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2}, proceedings_a={COMPLEX PART 2}, year={2012}, month={5}, keywords={Search algorithms betweenness centrality distributions}, doi={10.1007/978-3-642-02469-6_49} }- Parongama Sen
Year: 2012
Funnelling Effect in Networks
COMPLEX PART 2
Springer
DOI: 10.1007/978-3-642-02469-6_49
Abstract
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 of a node as the fraction of successful dynamic paths through it with a fixed target. The distribution () of the fraction of nodes with funnelling capacity 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 = ( = 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 () ∝ , increases linearly with initially and then attains a constant value. It shows a power law behaviour, , with the number of nodes where is weakly dependent on for > 2.2. The latter variation is also independent of the number of searches. On stretched exponential networks with , is strongly dependent on . The funnelling distribution for a model social network, where the question of funnelling is most relevant, is also investigated.