Asymptotic Behaviour of Gossip Processes and Small-World Networks
2013 ◽
Vol 45
(4)
◽
pp. 981-1010
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Keyword(s):
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.
2013 ◽
Vol 45
(04)
◽
pp. 981-1010
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2004 ◽
Vol 15
(06)
◽
pp. 755-765
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2012 ◽
Vol 2012
◽
pp. 1-18
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2016 ◽
Vol 20
(1)
◽
pp. 149-173
◽
2007 ◽
Vol 17
(07)
◽
pp. 2331-2342
◽
2001 ◽
Vol 04
(02n03)
◽
pp. 207-226
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Keyword(s):