Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2

Research Article

Funnelling Effect in Networks

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  • @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
Parongama Sen1,*
  • 1: University of Calcutta
*Contact email: psphy@caluniv.ac.in

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.