The Duality of Persons and Groups

Abstract

metaphor of classical theory concerning of persons within groups and of groups within individual is translated into set of techniques to aid in empirical of interpenetration of networks of interpersonal ties and networks of intergroup ties. These techniques are useful in'the study of director interlocks, clique structures, organizations within community and national power structures, and other collectivities which share members. network analysis suggested in this paper is compared to and contrasted with sociometric approaches and is applied to study by Davis et al. (1941) of participation of eighteen women. Consider metaphor which has often appeared in sociological literature but has remained largely unexploited in empirical work. Individuals come together (or, metaphorically, intersect one another) within groups, which are collectivities based on shared interests, personal affinities, or ascribed status of members who participate regularly in collective activities. At same time, particular patterning of an individual's affiliations (or of groups within person) defines his points of reference and (at least partially) determines his individuality.1 following discussion consists of translation of this metaphor into set of techniques which aid in empirical of interpenetration of networks of persons and networks of groups that they comprise. My usage of term group is restrictive in that I consider only those groups for which membership lists are available-through published sources, reconstruction from field observation or interviews, or by any other means. Such groups include corporation boards of directors (J. Levine, 1972), organizations within community or national power structure (Lieberson, 1971; Perrucci and Pilisuk, 1970), cliques or organizations in high school (Bonacich, 1972; Coleman, 1961), and political factions. Donald Levine (1959:19-22) writes that the concept of is key underlying Simmel's thought. Levine explicates Simmel's as the assumption that subsistence of any aspect of human life depends on coexistence of diametrically opposed elements. My own usage of comparable term is specified with respect to Equations 3 and 4 below.2 THE BASIC CONCEPTION Consider set of individuals and set of groups such that value of tie between any two individuals is defined as number of groups of which they both are members. value of tie between any two groups is de* For their criticism and encouragement, I am indebted to Harrison White, Gregory Heil, Francois Lorrain, and Scott Boorman. For seminars which first introduced me to Simmel's thought, I am indebted to Kurt H. Wolff. Thanks are due Professor White for support through NSF Grant GS-2689. 1 Simmel (1955) entitled one of his essays The Intersection of Social Circles, but Reinhard Bendix changed title in translation because a literal translation of this phrase is almost meaningless Simmel often plays with geometric analogies; it has seemed advisable to me to minimize this play with words . (Simmel, 1955:125). For an assertion that Simmel's original title is not at all inappropriate, see Walter's essay (1959). For more complete explication of dualism inherent in Simmel's thought, see essays by D. Levine, Lipman, and Tenbruck in Wolff (1959). similar metaphor was put forward in America by Charles H. Cooley (1902:148), who wrote that A man may be regarded as point of intersection of an indefinite number of circles representing groups, having as many arcs passing through him as there are groups. Much later, Sorokin (1947:345) observed that the individual has as many egos as there are different groups and strata with which he is connected. On much neglected development of concept of social circle since Simmel's writings, see Kadushin (1966). 2The directional duality principle enunciated by Harary et al. (1965) is to be distinguished from my conception. former consists in reversing directionality of lines in graph; in method of this paper, lines in one graph are transformed into points of its dual graph, and vice versa.