***** To join INSNA, visit http://www.insna.org ***** Dear Socnetters I used photos of 7 young women in my very old empirical study of structural balance in signed graphs. Tn that study 45 female students were informed that the women in the pictures marked A,B,C,D,E,F,G work together (actually, I found the photos of anonymous persons in a weekly newspaper for women; the readers were invited to assess for fun psychological traits of people from their photos) Each student obtained the set of 7 cards with the photos and a form in which a graphical scale looking more or less like this |_---__--__-__|__+__++__+++_| was printed next to each of 21 pairs of symbols AB, AC,…., FG (the pairs were listed in a random order rather than lexicographically). The subject’s task for each pair was to pick the respective two pictures from the set, look at them and guess the sign (but putting a tick on the left or right segment of the scale), of an emotional tie that must have arisen between two women when they had to meet face-to-face at work. Having ignored the intensity of liking/disliking, I obtained the set of 45 7-point complete signed graphs. My aim was to test if there is a tendency for structural balance in the data. Concretely, I wanted to check if the mean number of negative triangles in the empirical structures was significantly lower than in randomly generated structures (the probability of + in any pair being equal to ˝ and under independent assignment of signs to pairs). At the second step of my study I asked each subject to guess the sign of her relationship with women A….G, if she had to join the group as its 8th member H. My aim was to test if the degree of imbalance in the 7-point structure depends on the degree of imbalance in triangles containing H (as the ‘focal person’ as Heider would say). This problem was inspired by a theorem by Claude Flament (the author of ‘'Applications of Graph Theory to Group Structure'’, 1963). He proved that any n-point complete signed graph is balanced (that is, all triangles are positive) iff all triangles containing one node are positive. I wonder if any similar study has ever been done. My own research remains unpublished. It was reported only in a section of my Ph.D thesis (1982, in Polish). I lost my interest in empirical applications of signed graphs, when I plunged totally into mathematical theory of signed graphs (see my papers in Mathematiques et Sciences Humaines 1976, in French, and in the J. of Graph Theory, 1980). With best regards Tadeusz Sozanski _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.