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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.

Bill

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