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Haiko,

Your idea "smells" almost like so-called Segregation Matrix Index
developed by Freshtman (Fershtman, M., 1997. Cohesive group
segregation detection in a social network by the Segregation Matrix
Index. Social Networks 19, 193207.)

Best,
Michal


On Fri, Jan 17, 2014 at 1:56 PM, Lietz, Haiko <[log in to unmask]> wrote:
> ***** To join INSNA, visit http://www.insna.org *****
> Hi Kerstin, all,
>
> I've been thinking about the same problem recently, and I came up with the
> idea to use inter-group densities as they are normalized by the number of
> possible ties:
>
> Suppose you have a quadratic density matrix where rows i and columns j are
> groups and cells give densities. In the diagonal cells j=i you will have
> intra-group densities and in the other cells j!=i inter-group densities. You
> get this matrix in Ucinet if you run Network > Cohesion > Density > Density
> by Groups (the density matrix has the ending "-den").
>
> To get a relative measure, divide cell ij (j!=i) by the corresponding
> diagonal value of row i. In the resultiing matrix, the diagonal will have
> values = 1, all other cells will tell if the inter-group density is smaller
> (<1) or larger (>1) than the corresponding intra-group density. Values x
> will be in the interval [0, INF].
>
> If you want, you can transform x using the function f(x)=(x-1)/(x+1). Then
> they will be in the interval [-1,1], just like the E-I Index.
>
> For my data, the difference is huge.
>
> Does anybody know if this measure has been discribed in the literature? Or
> similar thoughts? I'd be happy to know...
>
> Best regards
>
> Haiko
>
>
> ________________________________
> Von: Social Networks Discussion Forum [[log in to unmask]]" im Auftrag von
> "Kerstin Sailer [[log in to unmask]]
> Gesendet: Freitag, 17. Januar 2014 13:03
> An: [log in to unmask]
> Betreff: [SOCNET] Clustering of networks / comparison across organisations
>
> ***** To join INSNA, visit http://www.insna.org ***** Dear All,
>
> I would like to do a comparison of different organisations and their network
> structures (nodes are people, ties are frequency and usefulness of contacts,
> sizes vary significantly from n=100 to n=1000; data is survey-generated; key
> question was to identify the top 25 contacts from a list of everyone in the
> organisation and then give details on these contacts).
>
> One of the metrics I would like to compare (and where comparison is not
> straightforward at all, hence my email to ask for help / advice) is the E-I
> index, i.e. the degree to which contacts are within teams or across teams.
>
> The difficulty is that team sizes and numbers of teams within an
> organisation differ so much. For instance if organisation A has 10 teams of
> 10 members each, every participant would have to nominate members from
> outside their team to come up with 25 top contacts, hence the degree of
> external contact might be higher by default than for an organisation B with
> 2 teams of 50 members each, where each participant could possibly nominate
> all 25 top contacts within their own team.
> This is further complicated by the fact that not everyone participated in
> the survey (i.e. missing ties), that not everyone nominated 25 people (most
> people don't count and just use this as a rough guideline, or insist on
> nominating fewer or more), so outdegree is not always 25 for each member and
> of course this could vary by team as well (so members of one team, e.g. HR
> might nominate more people disproportionately if compared to the
> organisation's average because of their outreach role).
>
> Now, if anyone has come across any discussion of those problems in the
> literature, or anyone mathematically minded on the list has an idea on how
> to normalise these metrics so that they become comparable, I'd be very happy
> to hear about it!
>
> Thanks in advance!
> Best,
> Kerstin
>
> --
> Dr Kerstin Sailer
> Lecturer in Complex Buildings
>
> The Bartlett School of Graduate Studies
> Faculty of the Built Environment
> University College London (UCL)
> 14 Upper Woburn Place
> London WC1H 0NN UK
>
> T: +44 (0) 20 3108 9031
> E: [log in to unmask]
> W: http://www.bartlett.ucl.ac.uk/graduate
> W: http://www.bartlett.ucl.ac.uk/people/?school=gs&upi=KSAIL15
>
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