3 - Signed graphs

Summary

The human mind arranges phenomena by a constant process of cognition, identification and polarization. Calling a certain object black presupposes both an identification of this object with other objects called black and a contradistinction of this object to other objects called white. Things do not have absolute self-sustaining properties. The latter are always a matter of relative position.

Jan Pouwer, “Towards a configurational approach to society and culture in New Guinea”

New Guinea alliance systems have been characterized by such notions as “fields of warfare” (A. Strathern 1971), “zones of interaction” (Berndt 1964), and “clusters” of clans (Ryan 1959). In his analysis of the structure of feasting and warfare among the Polopa of Highland New Guinea, D. J. J. Brown (1979) uses a metaphor based on a relation of coloring to describe the intertribal pattern of friendship and enmity:

In Polopa conception, the enemies of enemies (and allies of allies) are always allies, by definition. When visiting communities unknown to my companions (in making a survey of the Polopa area), their first concern was to establish whether or not they had allies or enemies in common, and if not they prevailed on me to move on. They did not recognize the possibility of neutrality. Some results of the survey are shown in the accompanying map… of the communities of Polopa and their immediate neighbors. For convenience the communities are color-coded, marking the position of each by an R (red) or G (green): any two of the same color are allies and of different colors enemies. Notice that two colors only are sufficient to complete the pattern. It has a patchwork quality, but of red and green only. […]