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Hi John,

I might have missed some important detail but to me it sounds as if the situation you describe is actually one of an affiliation network. Some people would argue that most networks are in fact artifacts of underlying bi-partite networks (others that person-person ties are ties in the own right - and some that it is a combination of both) and comember-ship in a team does, as you point out, induce cliques in the one-mode projection of the bipartite network.  Whatever your view, it is often instructive to study the network in its most basic, person by affiliation, form.

Some good references are
Borgatti, S.P., Everett, M.G., 1997. Network analysis of 2-mode data. Social Networks
19, 243–269.
Breiger, R.L., Pattison, P.E., 1986. Cumulated social roles—the duality of persons and
their algebras. Social Networks 8, 215–256.
Wang, P., Sharpe, K., Robins, G.L., Pattison, P.E., 2009. Exponential random graph (p*)
models for affiliation networks. Social Networks 31, 12–25.

and the references therein. Most bipartite networks are by construction undirected (two offecnders co-offending in an offence is meaningfull only in an undirected sense).

One reason why it is good to work directly with the bipartite network is that it preserves all the relevant information and you won't draw sputious conclusions such as inferrin that there is an endogenous clustering between people (or teams) based on the unimodal projection when this is merely reflecting the fact that some teams (people) have many members (are members of many teams).

j.
________________________________________
From: Social Networks Discussion Forum [[log in to unmask]] On Behalf Of John McCreery [[log in to unmask]]
Sent: 28 March 2011 14:53
To: [log in to unmask]
Subject: Re: [SOCNET] Cocitation equivalent for undirected networks?

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Mark,

Thank you very much. Allow me to put in a plug for your book. Even for a latecomer (independent scholar, anthropologist, age 67) to network analysis learning or relearning the necessary math as he goes along, it is admirably clear and easy to follow. I also have the new Jackson and Easley and Kleinberg books. Both are also excellent books, but the former in particular seems to me to rush the mathematical fences a bit too quickly for someone who doesn't know the math well before he begins to read it. You seem to me to have struck just the right balance.

Thank you again. Respectfully yours,

John McCreery

Sent from my iPad

On 2011/03/28, at 22:35, Mark Newman <[log in to unmask]> wrote:

> *****  To join INSNA, visit http://www.insna.org  *****
>
> The concept you're talking about is often called "structural equivalence".  Since I gather you have a copy of my book, you can read about it in Section 7.12, although there are a number of excellent texts available on social network analysis that also offer good discussions.
>
> Mark
>
>
>
> On 03/28/2011 07:43 AM, John McCreery wrote:
>> ***** To join INSNA, visit http://www.insna.org ***** I am reading
>> M.E.H.Newman's /Networks: An Introduction/ and have reached page 114
>> where the author defined cocitation for directed networks: "The
>> /cocitation/ of two vertices/ i/ and /j/ in a directed network is the
>> number of vertices that have outgoing edges pointing to both /i/ and
>> /j/." I am wondering if anyone has done research using an analogous
>> measure for undirected networks.
>>
>> I wonder if we might learn something important about ties between teams
>> if we were able to measure the number of vertices (= team members) with
>> edges linking them to both /i/ and /j /even if /i/ and /j /are not
>> linked to each other.
>>
>> I ask because, to me at least, an interesting problem in working with
>> networks connecting individual members of teams is that teams, by
>> definition, are cliques, which means that every member of a team is,
>> ipso facto, linked to every other. But, at least in the advertising
>> business from which my data come, team members to do always work with
>> each other. An individual may belong to more than one team. Thus, at one
>> extreme, a team may be composed of people who have never worked together
>> before or, at the other extreme, people who always work together, with
>> every possible variation in between. Being able to identify and measure
>> what we might call /co-comember /connections might lead to interesting
>> results.
>>
>> Any and all comments and suggestions are welcome.
>>
>> John McCreery
>> The Word Works, Ltd., Yokohama, JAPAN
>> Tel. +81-45-314-9324
>> [log in to unmask] <mailto:[log in to unmask]>
>> http://www.wordworks.jp/
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