Linton C. Freeman

Centrality in social networks conceptual clarification

Abstract The intuitive background for measures of structural centrality in social networks is reviewed and existing measures are evaluated in terms of their consistency with intuitions and their interpretability. Three distinct intuitive conceptions of centrality are uncovered and existing measures are refined to embody these conceptions. Three measures are developed for each concept, one absolute and one relative measure of the centrality of positions in a network, and one reflecting the degree of centralization of the entire network. The implications of these measures for the experimental study of small groups is examined.

A set of measures of centrality based on betweenness

A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.

Centrality in valued graphs: A measure of betweenness based on network flow

A new measure of centrality, C,, is introduced. It is based on the concept of network flows. While conceptually similar to Freeman’s original measure, Ca, the new measure differs from the original in two important ways. First, C, is defined for both valued and non-valued graphs. This makes C, applicable to a wider variety of network datasets. Second, the computation of C, is not based on geodesic paths as is C, but on all the independent paths between all pairs of points in the network.

Centrality in social networks: ii. experimental results

Abstract Three competing hypotheses about structural centrality are explored by means of a replication of the early MIT experiments on communication structure and group problem-solving. It is shown that although two of the three kinds of measures of centrality have a demonstrable effect on individual responses and group processes, the classic measure of centrality based on distance is unrelated to any experimental variable. A suggestion is made that the positive results provided by distance-based centrality in earlier experiments is an artifact of the particular structures chosen for experimentation.

The Sociological Concept of "Group": An Empirical Test of Two Models

Two models of the structural form of small, informal groups are compared. One, derived by Winship, requires that patterns of social affiliation be strictly transitive. The other, based on Granovetters ideas about weak and strong ties, requires only a special limited form of transitivity. When these alternative models are tested with data on human interaction, it turns out that the Winship model does not fit the data but that the model developed from Granovetters work does.

Research methods in social network analysis

Based on a conference held in Laguna Beach, CA, 1980. Comprises 14 essays on network representations and boundaries, relational structure, clustering and positioning of actors. No index. Annotation copyright Book News, Inc. Portland, Or.

Filling in the blanks: a theory of cognitive categories and the structure of social affiliation

This paper shows that people are aware of who is affiliated with whom in their immediate social world. Their perceptions of the patterning oh affiliation, however, do not correspond to the patterning actually displayed by interacting humans. Affiliation is not categorical; perceptions of affiliation are, however. On the basis of experimental evidence about errors in learning simple social structures, a theory that accounts for this discrepancy is proposed. This theory suggests that people impose a categorical form on noncategorical affiliation patterns by a process of filling in the blanks in their experience

The gatekeeper, pair-dependency and structural centrality

This is a note to introduce a new measure of a kind of structural centrality called pair-dependency. Pair-dependency explicates the centrality-related notion of the gatekeeper. Moreover, it turns out to be a fundamental structural property of communication networks that provides the basis for the derivation of two standard measures of structural centrality.

Segregation in Social Networks

The intuitive literature on segregation is reviewed and a segregation measure, S, is constructed to embody existing intuitions. S measures segregation over a network of symmetrical social relations. Distributional problems are explored and two kinds of applications are illustrated.

Finding an appropriate order for a hierarchy based on probabilistic dominance

Methods of ranking individuals in a dominance hierarchy that use transitivity of relationships may obscure irregularities. Furthermore, these methods use only a small proportion of the information available from dominance encounters. This paper presents an intuitively appealing and easily implemented alternative to existing methods for ordering dominance data, developed from the work of Batchelder et al. (1992 Journal of Mathematical Psychology36, 185-212). The procedure presented here is based on a mathematical model of paired comparisons and it involves only simple estimation procedures. We illustrate its use with data on dominance among red deer Cervus elaphus, stags. The results indicate that dominance relationships are well characterized by the scale values that the model provides, and, because the method provides predictions for all pairings of animals, dominance predictions also exist for pairs of animals that have yet to be observed. Moreover, the dominance outcomes predicted by the model using the order scale are highly correlated with actual dominance observations at all levels. Overall, the procedure described provides a solution to the problem of identifying an appropriate order for a near-linear dominance hierarchy. Copyright 1999 The Association for the Study of Animal Behaviour.