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Dear Socnetters

When you try to apply signed graphs to model macrosystems like the system 
of political actors fighting/cooperating in the Middle East, the first
step you  must make is to identify the set of actors involved in the
process of creating and changing bilateral relations. This step may often
appear most difficult as it requires more substantive than methological
competence.

The last chapter of my Ph.D. dissertation (1982, unpublished, in Polish)
discusses a wide range of applications of the theory of signed graphs. In
particular, I presented in there my own  analysis of the Falklands War
which broke ou when I was to finish my thesis. I was inspired by Harary's
paper ('A structural analysis of the situation in the Middle East in
1956', J. of Conflict Resolution, 1961). My strategy for defining the set
of political actors was to represent  macropolitical structure as
faithfully as possible but my aim was also to minimize as much as possible
the number of actors so that I could  'manually' compute indexes of
imbalance at each stage of the process.

My decision was to stay with 7 actors: (1) A (Argentina); (2) GB (Great
Britain); (3) USA; (4)SU (Soviet Union); (5) WE (Western Europe); (6) L
('left' Latin American States); (7) R ('right', etc.). Once the
mathematical part of my thesis dealt mainly with COMPLETE signed
undirected graphs, I decided to mark each of 21 lines of the complete
7-point graph with plus or minus. I used two  measures of imbalance: the
number of negative triangle (cycle of length 3) and 'line index of
imbalance' (the minimum number of lines such that a sign change in each
restores balance).

The system I defined was initually balanced, the first step in the process
of structure evolution was the change of sign of the line A-SU from - to +
(politically, Argentina helped SU, with selling its food products, to
resist US sanctions that followed SU's invasion in Afganistan). The change
resulted in imbalance and further changes increased the degree of
imbalance to a point  from which the system moved back to a new state of
balance.

There are many substantive areas within the social sciences where SIGNED
graphs have been or can be applied... Shall we see a revival of interest
in this kind of relational models? Pat Doreian could probably tell more
about it. Having published two mathematical papers on signed graphs (in
Mathematiques et Science Humaines, 1976, and in J. of Graph Theory, 1980)
long time ago, I have not since then watched further developments in this
field.

Tad Sozanski

http://www.cyf-kr.edu.pl/~ussozans/

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