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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

Gesendet: Freitag, 17. Januar 2014 13:03
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!

Best,
Kerstin
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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