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Hi - 

I'd argue that stability is distinct from structural cohesion -- the
substantive point is to be able to ask theoretically whether membership in a
particular network structure leads to stability in relations/membership
(particularly beyond dyadic features) rather than building stability into
the measure/meaning of the tie.  One of the strong advantages of a network
approach to cohesion over the LOOOONNNNNG and confused literature in
sociology on "group cohesion," is that we don't build the outcome (feeling
good, performance, etc. etc.) into the definition of cohesion, but instead
treat it as an outcome for testing. 

The node-cohesion metric will remain stable if the group stays the same over
time. If all members of the group maintain their same tie pattern from t1 to
t2 -- as suggested in your example --  then their k-connected set will be
the same regardless of what happens elsewhere in the graph.  This is the
advantage of a hard-coded model rather than a relative-density model.
(there are obvious tradeoffs of course -- fluctuations due to edge-level
measurement error being a strong one).  If cohesion tracks the difficult in
separating pairs (or equivalently the number of unique routes for
transmission); this is exactly what you want.  If actors add ties outside
their group, then the k-connected set is still stable as a minimum kernel of
membership. That is, others may be added to the group if they add ties to
new nodes, but without dropping ties inside the group, the k-connectivity
remains the same.  

If you do what to respect time directly, there are ways to do so. One
approach our group is working on is to treat time *as* structure by building
"identity edges" linking nodes to themselves over time (if interested, email
off line and I'll send a draft) -- one can then cluster the entire
"link-time" graph for temporally cohesive regions.

Also on the notion of time-specific modularity; Peter Mucha and colleagues
have a new partitioning algorithm out that takes temporal patterns directly
into account.  

Best,
Jim 

-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
Behalf Of Balazs Vedres
Sent: Tuesday, January 05, 2010 9:38 AM
To: [log in to unmask]
Subject: Re: community identification algorithms

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

I see two concerns with current conceptions of cohesion:

1. Are overlaps allowed or made sense of?

Most methods allow overlap, but in their application there is very little
mentioned about the phenomenon of overlapping. Is it an accident? Does it
have benefits? Are there meaningful connections to agency?

2. Does it work with dynamic data?

Most methods are incapacitated in a dynamic framework. Let's say a dense,
cohesive group A stays the same between t1 and t2 (same members, and the
same ties among them). Now, most methods (including most new ones like Moody
and White) would not recognize that group A stayed the same, if the network
environment changes (it becomes denser or sparser for example). In other
words, I see no other solution in a dynamic framework beyond local
algorithms (like the clique percolation method). Otherwise how do you
separate network change from methodological artifact?  

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