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Re: [igraph] about degree.sequence.game and configuration model

From: Tamas Nepusz
Subject: Re: [igraph] about degree.sequence.game and configuration model
Date: Tue, 21 Sep 2010 14:13:48 +0100
User-agent: Mutt/1.5.20 (2009-06-14)

> The "vl" method might be equivalent to the configuration model,
> depending on whether that allows unconnected graphs or not.
AFAIK the configuration model allows unconnected graphs and
multiple/loop edges as well, so I'd say that the "simple" method is
closer to the configuration model than the VL method.

Also, note that there are two different models in the literature, both
referred to as the "configuration model". One is essentially equivalent
to the "simple" method: every vertex i gets d_i "stubs" (where d_i is
the prescribed degree of vertex i), and then these stubs are selected
randomly and connected. The other configuration model is different in
the sense that it prescribes the *expected* degree of each vertex only.
Edges are then generated independently, where the probability of the
edge  between vertices i and j is (d_i * d_j) / (sum_k d_k). This latter
model is not implemented in igraph, and it does not guarantee that the
degrees will be equal to the prescribed degrees *exactly*, it prescribes
the expected values of the degrees only.


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