A major part of human behavior occurs in groups. Many different kinds of groups and probably even more definitions of human groups exist (among others: Freeman, 1992; Homans, 1950; Shaw, 1981). In the field of social networks in particular, many researchers have attempted to provide a formal definition of such groups (among others: Alba, 1973; Luce and Perry, 1949; Mokken, 1979). We focus on naturally emerging and freely forming small social groups, friendship groups in particular. From all different kinds of groups, these are most difficult to define, because they lack any pre-defined assignment of members (such as in experimental groups, task-oriented groups, problemsolving groups, therapeutical groups, groups in decision making processes and so on (Mullen, 1987)). The motives for group membership concern some form of satisfaction of social needs and related drives that are purely voluntary. A group that emerges accordingly is a very important aggregation from the view of its individual members. How it provides them social identity, and how their behaviors, attitudes, and opinions are shaped by the group are processes frequently studied in the field of social psychology and social networks (Erickson, 1988; Mullen and Goethals, 1987; Tajfel and Turner, 1986). In these studies, however, how these groups come into existence is ignored usually. We think that in order to understand how group membership influences individuals, it is at least as important to understand how the group in one way or the other has been 'constructed' by the saIne individuals. The emergence of such groups, and especially its related structural characteristics, is the main problem we address here.