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Re: Modularity Q

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Tue, 4 Jun 2013 15:57:16 +0200

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 ```***** To join INSNA, visit http://www.insna.org ***** Per, ad 1. The matrix eii will be symmetric because the network Newman&Girvan analyze is undirected. The assortativity coefficient on which Q is based (see ref. 34 in N&G paper you refer to) was in fact developed for directed networks, so that eii does not have to be symmetric. ad 2. ai*ai make sense as a null model because it corresponds to "proportionate mixing": fraction of ties between groups i and j is proportional to the number of links they have. See Koehly, L. M., Goodreau, S. M., Morris, M., 2004. Exponential family models for sampled and census network data. Sociological Methodology 34, 241–270 for a nice discussion of possible null models for mixing matrices. Your null model corresponds to one of the conditional log-linear models discussed in section 3.1 of that paper. The term "proportionate mixing", as far as I know, comes from Nold, A., 1980. Heterogeneity in disease-transmission modelling. Mathematical Biosciences 52 (3–4), 227–240. I hope this helps. Best, Michal On Tue, Jun 4, 2013 at 3:27 PM, Kropp Per <[log in to unmask]> wrote: > ***** To join INSNA, visit http://www.insna.org ***** > Hello everybody, > I use a formula from Newman/Girvan (Phys. Rev. E 69 (2004) 026113) to > calculate Q=SUMi(eii-ai*ai) with ai=SUMj(eij) from the k x k symmetric > matrix e. eii is the fraction of links within the cluster k and ai is the > row (or column) sum. Very easy to implement in standard statistical > packages. Here are my questions: > 1. Why has matrix e to be symmetric? > 2. Why can ai*ai be characterized as an appropriate null model? > (Both are questions from a reviewer ;-)) > Best regards to the specialists > Per > _____________ > Dr. Per Kropp > Institute for Employment Research > Regional Research Network > Frau-von-Selmnitz-Str. 6, D-06110 Halle > Germany > Phone: +49/345-1332-236 (secretary: -255; fax: -555) > mail: [log in to unmask] > www.iab.de/iab-sachsen-anhalt-thueringen > > > > _____________________________________________________________________ SOCNET > is a service of INSNA, the professional association for social network > researchers (http://www.insna.org). To unsubscribe, send an email message to > [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of > the message. _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.```