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Asymptotic Behaviour of Gossip Processes and Small-World Networks
Published online by Cambridge University Press: 04 January 2016
Abstract
Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.
- Type
- General Applied Probability
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- Copyright
- © Applied Probability Trust
Footnotes
ADB was Saw Swee Hock Professor at the National University of Singapore while part of this work was carried out. Work supported in part by the Australian Research Council grants DP120102728 and DP120102398.
Supported in part by the EPSRC and BBSRC through OCISB.
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