A distance model for sociometric structure†

Research supported in part by National Science Foundation Grants SOC 73–05489 to Carnegie‐Mellon University and GS‐2689 to Harvard University, and a National Science Foundation Graduate Fellowship.

The conceptual and mathematical framework of a general model for distance within sociometric structure is described. The model characterizes “balance” in terms of the triangle inequality, in which the distance between two people (A and C) should be less than or equal to the sum of the distances to a third person (B), i.e., d (A,C) ≤ d (A,B) + d (B,C). The notion of addition of distances is developed. Different ways of adding distances result in different models of sociometric structure. Two families of models for symmetric graphs are discussed. The general model is extended to asymmetric graphs by generalizing the notion of transitivity. The model's potential for resolving a problem of the transitivity’ model is then discussed. The general model provides a means of examining the relationship between stratification and clustering in the structure of groups.

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Research supported in part by National Science Foundation Grants SOC 73–05489 to Carnegie‐Mellon University and GS‐2689 to Harvard University, and a National Science Foundation Graduate Fellowship.