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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 <[log in to unmask]> wrote:

> ***** To join INSNA, visit http://www.insna.org *****
> 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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