Funnelling related phase transitions in networks

Details Funnelling related phase transitions in networks Funnelling related phase transitions in networks

2008-01-02

arxiv.org/abs/0801.0370v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, revtex4, 6 figures This paper is withdrawn as it required some correction

Scientific paper

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. We claim that there is a funnelling effect if the distribution $D(f)$ of the fraction of nodes with funnelling capacity $f$ shows a power law behaviour. We find that a transition from a search with funnelling effect to that without any such effect can exist and is driven by the parameters defining the network.

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