Showing papers by "Linton C. Freeman published in 1993"
TL;DR: A new solution to the old problem of partitioning a matrix of social proximities into groups is proposed, drawing on a heuristic developed in computer science, the simple genetic algorithm.
Abstract: A new solution to the old problem of partitioning a matrix of social proximities into groups is proposed It draws on a heuristic developed in computer science, the simple genetic algorithm The algorithm is described and its utility is demonstrated with applications to three standard data sets
21 citations
TL;DR: Eden and Borgatti as mentioned in this paper generalized their earlier definition of role coloring of graphs and extended their previous results to demonstrate that colorings can be used to find regular partitionings in digraphs, networks and hypergraphs.
14 citations
TL;DR: Dunbar's notion that the limit on an individual's information processing capacity imposes a limit on group size depends on how the group is conceived as discussed by the authors, and there is no necessary connection between the number of others with whom an individual has a personal tie and the sizes of the "groups" in the sense they were defined by Dunbar.
Abstract: Dunbar's basic idea that neocortical size constrains "the number of relationships an animal can keep track of in a complex, continually changing social world" is appealing, but the notion that such a limit leads to a constraint on the size of the social groups in which the individual is embedded is less so. The problem is in Dunbar's casual treatment of groups. Over 30 years ago Floyd Allport (1961, p. 195) pointed out that because "a group is a phenomenon so familiar to everyone that it is not a question of what 3 group is, but only of how it works," researchers had simply "assumed the existence of groups." This is precisely what Dunbar has done. Dunbar's notion that the limit on an individual's information processing capacity imposes a limit on group size depends on how the group is conceived. He defines a group as a subset of a population of conspecifics that "interacts on a sufficiently regular basis to have strong bonds based on direct personal knowledge." For their knowledge to be personal, each individual must interact "on a sufficiently regular basis" with each and every other individual in the group. A subset that is maximal with respect to that property has been formally dubbed a "chque" (Luce & Perry 1949). The properties of chques can be specified in exact terms. Given a finite collection of individuals A = (a,b,c, . . . ) along with a symmetric relation / that links those pairs of individuals in A that interact on a sufficiently regular basis to have "strong bonds," suppose that each individual in A has the relation / with n other individuals; n is then the number of others with whom an individual has a "personal" tie. Suppose further that we find a clique in A of size m. If Dunbar is right, there must be a relationship between n and m. But the value of m only sets a lower limit on n, n a m — 1. The upper limit of n depends on the arrangement of the ties linking individuals in A, and there is no necessary connection between the number of others with whom an individual has a personal tie and the sizes of the "groups" in the sense they were defined by Dunbar. Dunbar may, however, have had other (unstated) restrictions in mind when he talked about groups. In his groups, for example, he may have assumed that "friends of friends are fiiends." In that case, the relation / would be transitive and each group would be a special kind of clique that Davis (1967) called a cluster. All individuals within each cluster would be directly hnked, and no individuals falling in difiFerent clusters would be. In that case, n = m — 1, and individual network size would be inextricably tied to group size. But, at least in the case of human primates, interaction fi-equencies are certainly not transitive (Freeman 1992b). Humans do display some tendency to strain toward transitivity in
2 citations