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One can generate random networks conditional on the degree
distribution and the number of components. That way we
preserve degrees and component sizes but scramble everything
else there might be. See Maslov, Sneppen and Zaliznyak,
Pattern Detection in Complex Networks: Correlation Profile
of the Internet (2002), http://xxx.lanl.gov/abs/cond-mat/0205379
Basically, we repeatedly pick two non-incident edges (i.e.
those that don't share a vertex) at random and swap two
endpoints, making sure that this (1) does not create
self-loops; (2) neither it increases the number of
components if we want connected networks.
Graduate Fellow, ISERP and
Teaching Fellow, Dept. of Sociology
E-mail: gk297 at columbia.edu
Phone: +1 (212) 854 0367
On Tue, 18 Nov 2003, Bill Richards wrote:
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> A recent posting asked about generating a random network:
> "I would like to generate a random network, with a similar
> number of nodes and connection to the network I have
> created from field data, to compare the distance and
> clustering co-efficient of each. ... My network created
> from field data has no isolated nodes. However, when I ask
> Pajek to create a network with the same number of nodes
> and connections I get plenty of isolates, which apparently
> will not make a valid clustering co-efficient or distance
> comparison. ... Can anyone suggest a way of either
> generating a random network with a specified number of
> nodes and connections that has no isolates ... ?"
> This raises two new question:
> Is a "random" network still "random" if every node must
> have at least one connection to the rest of the network --
> in other words, if it must have no isolates, or, perhaps,
> it must be connected (there must be a path from each node
> to every other node)?
> What does it mean for a network to be "random"?
> Duncan Watts gives a very clear presentation of this issue
> on pages 43 to 68 of his excellent book Six Degrees: the
> science of a connected age.
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