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Hi Bob!

I'm afraid I'm not going to give you a direct answer to your questions.
Just a few hints..

Computationally the "advanced degree" you're asking might be easily
obtained in the following way:

Consider the 3-partite graph consisting of the 3 partite sets A1, A2 and
G, where A1 = A2 = A, the set of actors, and G the set of groups in which
actors are partitioned.

Then, if i is an actor and Gj is a group, the Gj-degree of i is the sume
of lines connecting i with Gj in the 3-partite graph. (Obviously,
degree(i) = sum(Gj).)

Now coming to your "visualization" question, I don't know if Pajek may do
the job automatically but certainly you can do it manually: Pajek allows
you to drag and change the coordinates of a node by keeping its links in
the new position.

However, a related theoretical remark could be made at this point. Let's
put signs on links according to whether nodes (actors) belong to the same
or different groups: a link is signed + if both nodes are actors in the
same group and - if not. Then if the graph is balanced (it contains no
negative cycles) we know from the Structure Theorem that a clustering
exists of the signed groups into components which are all linked in their
interior by + links and - links connect two different such components.

Thus, what remains to be seen from your data is whether your network is
indeed balanced (in the above sense) and whether the number of clusters
you obtain are exactly as many as your groups are. Or there are more
clusters than groups, which would mean that certain groups would be
decomposed in two (or more clusters) which are connected by paths of
length bigger or equal than 2 and through the "insertion" of clusters
composed of other groups.

I'm not sure if you're interested in such theoretical constructions but I
would be happy to discuss these issues with you if you do. Furthermore,
another unexplored (to my knowledge) question would be the blockmodeling
structure of connected clusters composed of actors belonging to the same
group.

Greetings,

--Moses

  M.A. Boudourides
  Associate Professor

  Department of Mathematics
  University of Patras
  265 00 Rio-Patras
  Greece

  Tel.: +30-2610-996318
  Fax:  +30-2610-996318, +30-2610-992965

  http://www.math.upatras.gr/~mboudour


On Fri, 6 Feb 2004, Bob Kijkuit wrote:

> *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****
>
> Dear Socnetters,
>
> Hope you do not consider this too much of a newbe question.
> I am trying to find a way (in UciNet or Pajek) to calculate a node's degree
> centrality that distinguishes between ties within a division and between
> divisions and companies. So say 'Mike' from the life sciences division
> reports to have four friends in his own division, two in the micro biology
> division and three in supplier "X". I could of course simply count, but that
> seems a bit much for around 150-200 people. Is there a way to use a
> attribute file to generate something like:
>
>         Life sciences   Micro biology   Supplier X
> Mike            4                       2                       3
>
> Maybe with a extra column on the percentage of ties in each group etc. It
> seems so extremely trivial that I cannot imagine that somebody has not done
> this before me.
>
> The other has to do with visualizing. How can I artificially cluster a group
> of nodes on the basis of the division or company they are in (without
> showing ties between people from similar divisions)? So that I get a network
> picture where Mike and his four friends from Life sciences are grouped and
> that his three supplier friends are grouped etc.
>
> Thanks in advance for any help,
> Bob
>
> --
> R.C. Kijkuit
>
> Department of Technology and Innovation
> Rotterdam School of Management/Faculteit Bedrijfskunde
> Erasmus University Rotterdam
>
> F3-65
> Postbus 1738
> 3000 DR Rotterdam
> The Netherlands
>
> Tel. + 31(0)10-4082544
> Fax. + 31(0)10-4089014
> E-mail: [log in to unmask]
>
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