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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?
  Thanks in advance...

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