***** To join INSNA, visit http://www.insna.org ***** 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, 193–207.) 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 > > _____________________________________________________________________ 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. _____________________________________________________________________ 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.