Showing papers by "Katherine Faust published in 1994"

Social Network Analysis: Methods and Applications

Abstract: Part I. Introduction: Networks, Relations, and Structure: 1. Relations and networks in the social and behavioral sciences 2. Social network data: collection and application Part II. Mathematical Representations of Social Networks: 3. Notation 4. Graphs and matrixes Part III. Structural and Locational Properties: 5. Centrality, prestige, and related actor and group measures 6. Structural balance, clusterability, and transitivity 7. Cohesive subgroups 8. Affiliations, co-memberships, and overlapping subgroups Part IV. Roles and Positions: 9. Structural equivalence 10. Blockmodels 11. Relational algebras 12. Network positions and roles Part V. Dyadic and Triadic Methods: 13. Dyads 14. Triads Part VI. Statistical Dyadic Interaction Models: 15. Statistical analysis of single relational networks 16. Stochastic blockmodels and goodness-of-fit indices Part VII. Epilogue: 17. Future directions.

Social Network Analysis: Social Network Analysis in the Social and Behavioral Sciences

Abstract: The notion of a social network and the methods of social network analysis have attracted considerable interest and curiosity from the social and behavioral science community in recent decades. Much of this interest can be attributed to the appealing focus of social network analysis on relationships among social entities, and on the patterns and implications of these relationships. Many researchers have realized that the network perspective allows new leverage for answering standard social and behavioral science research questions by giving precise formal definition to aspects of the political, economic, or social structural environment. From the view of social network analysis, the social environment can be expressed as patterns or regularities in relationships among interacting units. We will refer to the presence of regular patterns in relationship as structure . Throughout this book, we will refer to quantities that measure structure as structural variables . As the reader will see from the diversity of examples that we discuss, the relationships may be of many sorts: economic, political, interactional, or affective, to name but a few. The focus on relations, and the patterns of relations, requires a set of methods and analytic concepts that are distinct from the methods of traditional statistics and data analysis. The concepts, methods, and applications of social network analysis are the topic of this book. The focus of this book is on methods and models for analyzing social network data. To an extent perhaps unequaled in most other social science disciplines, social network methods have developed over the past fifty years as an integral part of advances in social theory, empirical research, and formal mathematics and statistics.

Social Network Analysis: Centrality and Prestige

Abstract: One of the primary uses of graph theory in social network analysis is the identification of the “most important” actors in a social network. In this chapter, we present and discuss a variety of measures designed to highlight the differences between important and non-important actors. Definitions of importance , or synonymously, prominence , have been offered by many writers. All such measures attempt to describe and measure properties of “actor location” in a social network. Actors who are the most important or the most prominent are usually located in strategic locations within the network. As far back as Moreno (1934), researchers have attempted to quantify the notions of sociometric “stars” and “isolates.” We will discuss the most noteworthy and substantively interesting definitions of importance or prominence along with the mathematical concepts that the various definitions have spawned. Among the definitions that we will discuss in this chapter are those based on degree, closeness, betweenness, information , and simply the differential status or rank of the actors. These definitions yield actor indices which attempt to quantify the prominence of an individual actor embedded in a network. The actor indices can also be aggregated across actors to obtain a single, group-level index which summarizes how variable or differentiated the set of actors is as a whole with respect to a given measure. We will show how to calculate both actor and group indices in this chapter.

Social Network Analysis: Affiliations and Overlapping Subgroups

Abstract: In this chapter we discuss methods for analyzing a special kind of twomode social network that represents the affiliation of a set of actors with a set of social occasions (or events) We will refer to these data as affiliation network data, or measurements on an affiliation variable This kind of two-mode network has also been called a membership network (Breiger 1974, 1990a) or hypernetwork (McPherson 1982), and the affiliation relation has also been referred to as an involvement relation (Freeman and White 1993) Affiliation Networks Affiliation networks differ in several important ways from the types of social networks we have discussed so far First, affiliation networks are two-mode networks, consisting of a set of actors and a set of events Second, affiliation networks describe collections of actors rather than simply ties between pairs of actors Both of these features of affiliation networks make their analysis and interpretation somewhat distinct from the analysis and interpretation of one-mode networks, and lead us to the special set of methods discussed in this chapter Among the important properties of affiliation networks that require special methods and interpretations are: Affiliation networks are two-mode networks Affiliation networks consist of subsets of actors, rather than simply pairs of actors Connections among members of one of the modes are based on linkages established through the second mode Affiliation networks allow one to study the dual perspectives of the actors and the events We will return to these ideas throughout this chapter

Social Network Analysis: Structural Balance and Transitivity

Abstract: One of the most important concepts to emerge from the early days of social network analysis was balance theory . The early focus in balance theory was on the cognition or awareness of sociometric relations, usually positive and negative affect relations such as friendship, liking, or disliking, from the perspective of an individual. The idea of balance arose in Fritz Heider's (1946) study of an individual's cognition or perception of social situations. Heider focused on a single individual and was concerned about how this individual's attitudes or opinions coincided with the attitudes or opinions of other “entities” or people. The entities could be not only people, but also objects or statements for which one might have opinions. He considered ties, which were signed, among a pair or a triple of entities. Specifically, Heider (1946) states: In the case of two entities, a balanced state exists if the [ties] between them [are] positive (or negative) in all aspects. … In the case of three entities, a balanced state exists if all three possible [ties] are positive in all respects, or if two are negative, and one positive, (page 110) For example, we can consider two individuals, focusing on one of them as primary, and their opinions about a statement, such as “We must protect the environment.” If both actors are friends, then they should react similarly to this statement — either both should oppose the statement (and hence, both have a negative opinion about it) or both should favor it (and have positive opinions).