Hi Muge,

Below is a part of a paper that we wrote with Joel Baum, Tim Rowley,
Huggy Rao and Henrich Greve. If you want the full paper, I can send it
or you could wait until this year's Academy of Management were we will
present it. It's entitled "Competing in Groups" and should be
forthcoming in the special issue of Managerial and Decision Economics
this or next year (in case you want to cite it).

We also use the frequency of contact as a Xij entry in a matrix.

Hope this helps.



Network Definition
Industry networks were defined based on memberships in underwriting
syndicates.  Networks were constructed from adjacency matrices capturing
the number of times each bank participated in a syndicate with each
other bank for two-year moving periods (i.e., 1952-53, 1953-54, 1954-55,
etc…).  We used two-year periods because syndicates can remain intact up
to six months or more prior to the date of the offering.  Consequently,
constructing the network based on one-year periods would represent the
network inaccurately because syndicates that conclude in a given year
may have been established in the prior year, but not measured in that
year.  Moreover, syndicate ties represent the visible manifestation of
relationships among banks.  Banks participating in syndicates together
in a given year are also likely to interact with each other in years
proximate to the syndicate.  Our two-year moving period approach to the
network's construction allows for this possibility.  These networks were
used to compute data on the characteristics of each bank's network
position in the second year of each two-year period.  Thus, the 1952-53
network was used to measure banks' network positions for 1953, the
1953-54 network for positions in 1954, etc.

Clique Definition

Cliques were also constructed based on syndicate ties.  We transformed
each two-year adjacency matrix into a similarity matrix, which we then
analyzed using hierarchical clustering techniques to form dendograms
from which to classify banks into cliques.  We defined cliques at
rescaled combining distance of 10 (the rescaled maximum was 25).  To
improve the reliability of the cliques, we then constructed new
adjacency matrices indicating how many years within a given five-year
period (e.g., 1952-1957, 1953-1958, and so on) each bank belonged to the
same clique as each other bank.  We then repeated the process using the
five-year clique matrices to identify cliques.  Finally, we constructed
a genealogy of the five-year cliques, linking them over time.  A clique
was considered ongoing from period t to period t+1 if it retained more
than 50% of its membership from the previous period; in most cases the
percentage was far higher.  Thus, if a clique identified from the
1952-57 clique adjacency matrix shared more than 50% of its members with
a clique identified from the 1953-58 clique adjacency matrix, we
considered the 1953-58 clique to be a continuation of the 1952-57

-----Original Message-----
From:   Muge Ozman
Sent:   Tue 6/4/2002 5:13 AM
To:     [log in to unmask]
Subject:             a question on clique overlaps

Dear All,
I am currently a Ph.D student at MERIT (Maastricht Economic Research
Institute on Innovation and Technology).

A current problem that i face in my thesis is about the clique overlap
issue. I want to obtain non-overlapping cliques, based on a weighted
adjacency matrix (weights being the frequency of interactions). I have
UCINET for 50x50 adjacency matrix to detect cliques, but i don't know
how i
can seperate them in the optimum way? (lets say i obtain 150 cliques,
is a great deal of overlap). Is there any algortihm, or software, or
or idea (anything!) that someone can offer?

Any opinions will be greatly appreciated.
Best Regards,
Muge Ozman

Maastricht University - MERIT
P.O. Box 616 6200MD
The Netherlands