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The software ORA (Organizational Risk Analyzer) available at www.casos.cs.cmu.edu has a Silo Index in the Subgroups Report.  The index is applied to the subgroup rather than the network as a whole.  This corrects your concern about two groups merging into one.  The index spans from 1 (all in-group ties, no out-group ties) to -1 (all out-group ties, no in-group ties).

Ian McCulloh

On Thu, Aug 29, 2013 at 9:04 PM, Justin Koonin wrote:
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Hi everyone,

I'm fairly new at SNA research and have a question about a possible index of collaboration between groups.

I have a graph whose nodes represent individuals in an organisation, and whose edge values represent some measure of collaboration between each pair of individuals

The individuals are grouped into different units. I would like to measure the extent of collaboration between different units.

My sense is to define a "collaboration index" =

(Sum of weights of edges between different units)/
(Total sum of weights of all edges)

Thus, if an organisation exists in silos (I.e no co-operation at all between members of different units) the collaboration index would be 0. On the other hand, if membership of a particular unit played no role at all in determining whom an individual works with, the collaboration index would be very close to 1.
This measure tends to favour many smaller units over a few larger ones, so possibly a better measure is

(Sum of weights of edges between different units)/ x (Number of pairs of individuals)/
(Total sum of weights of all edges)                            (Number of pairs of individuals in different units)

However neither of these measures is robust to changes in the structure of the units themselves.  For example, if two units are working closely together and decide to amalagamate into one bigger unit, the collaboration index would go down, which seems counterintuitive.

So I'd like to know if there are other, better, ways to measure this sort of thing?