Katherine Faust

Centrality in affiliation networks

This paper discusses the conceptualization, measurement, and interpretation of centrality in affiliation networks. Although centrality is a well-studied topic in social network analysis, and is one of the most widely used properties for studying affiliation networks, virtually all discussions of centrality and centralization have concerned themselves with one-mode networks. Bonacichs work on simultaneous group and individual centralities is a notable exception (Social Networks, 1991, 13, 155–168). I begin by outlining the distinctive features of affiliation networks and describe four motivations for centrality indices in affiliation networks. I then consider properties of some existing centrality indices for affiliation networks, including the relationship between centralities for actors and events in these networks, and present a new conceptualization of centrality that builds on the formal properties of affiliation networks and captures important theoretical insights about the positions of actors and events in these networks. These centralities are then illustrated on Galaskiewiczs data on club and board memberships of a sample of corporate executive officers (Social Organization of an Urban Grants Economy. New York: Academic Press, 1985). The conclusion to this paper discusses strengths and weaknesses of centrality indices when applied to affiliation networks.

Networks and Contexts: Variation in the Structure of Social Ties1

A core axiom of sociology is that social structure affects and is affected by human behavior. The term “social structure” conveys two quite different meanings. One meaning is relational, involving networks of ties between individuals or groups of individuals. A second meaning refers to the contexts containing these individuals. Studies of neighborhood and community effects depend on variability in both types of social structure. Using data from multiple villages in Nang Rong, Thailand, this article documents substantial variability in network structure and shows that network structure covaries with context in meaningful ways, suggesting reciprocal effects of changes in both. Finally, it considers implications of variability in network structure, showing that social cohesion affects the likelihood of finding and interviewing former village residents.

Comparing Networks Across Space and Time, Size and Species

We describe and illustrate methodology for comparing networks from diverse settings. Our empirical base consists of 42 networks from four kinds of species (humans, nonhuman primates, nonprimate mammals, and birds) and covering distinct types of relations such as influence, grooming, and agonistic encounters. The general problem is to determine whether networks are similarly structured despite their surface differences. The methodology we propose is generally applicable to the characterization and comparison of network-level social structures across multiple settings, such as different organizations, communities, or social groups, and to the examination of sources of variability in network structure. We first fit a p* model (Wasserman and Pattison 1996) to each network to obtain estimates for effects of six structural properties on the probability of the graph. We then calculate predicted tie probabilities for each network, using both its own parameter estimates and the estimates from every other network in the collection. Comparison is based on the similarity between sets of predicted tie probabilities. We then use correspondence analysis to represent the similarities among all 42 networks and interpret the resulting configuration using information about the species and relations involved. Results show that similarities among the networks are due more to the kind of relation than to the kind of animal.

Comparison of methods for positional analysis: Structural and general equivalences

Abstract This paper explores the conceptualization and measurement of social position in relational data. It is argued that social positions are evidenced in the interactions among individuals, which are encoded in measured social relations. Given a set of measured relations the task is to reveal social positions which consist of groups of individuals wth similar patterns of relations. Methods based on two alternative approaches are discussed. The first set of approaches is based on structural equivalence, and locates groups of similar individuals based on the extent to which they share identical ties with identical others. A second set of approaches, here called general equivalences, locates groups of similar individuals based on their sharing of “types” of ties with “types” of others. Procedures based on these different approaches are described and applied to actual data and to a constructed example. Results suggest that these different approaches identify different kinds of social groups. It is argued that structural equivalence is an unsuitable basis for analysis of relational data if the goal is detection of social positions.

Building stochastic blockmodels

Abstract The literature devoted to the construction of stochastic blockmodels is relatively rare compared to that of the deterministic variety. In this paper, a general definition of a stochastic blockmodel is given and a number of techniques for building such blockmodels are presented. In the statistical approach, the likelihood ratio statistic provides a natural index to evaluate the fit of the model to the data. The model itself consists of a set of actors partitioned into positions with respect to a definition of equivalence, and a representation based on estimated probabilities. The specific statistical model that is used to illustrate the techniques is p1, which was first introduced as a method for stochastic blockmodeling by Fienberg and Wasserman (1981), and developed by Holland et al. (1983) and Wasserman and Anderson (1987).

7. Very Local Structure in Social Networks

Triadic configurations are fundamental to many social structural processes and provide the basis for a variety of social network theories and methodologies. This paper addresses the question of how much of the patterning of triads is accounted for by lower-order properties pertaining to nodes and dyads. The empirical base is a collection of 82 social networks representing a number of different species (humans, baboons, macaques, bison, cattle, goats, sparrows, caribou, and more) and an assortment of social relations (friendship, negative sentiments, choice of work partners, advice seeking, reported social interactions, victories in agonistic encounters, dominance, and co-observation). Methodology uses low dimensional representations of triad censuses for these social networks, as compared to censuses expected given four lower-order social network properties. Results show that triadic structure is largely accounted for by properties more local than triads: network density, nodal indegree and outdegree distributions, and the dyad census. These findings reinforce the observation that structural configurations that can be realized in empirical social networks are severely constrained by very local network properties, making some configurations extremely improbable.

Blockmodels: Interpretation and evaluation

Abstract Many methods for the description of social network structural properties are concerned with the dual notions of social position and social role . Common goals of these methods are to represent patterns in complex social network data in simplified form, to reveal sets of actors who are similarly embedded in networks of relations, and to describe the associations among relations in multirelational social networks. Often these representations take the form of a blockmodel . In a blockmodel actors are assigned to positions and network relations are presented among positions, rather than among actors. The literature on blockmodels is extensive and is overflowing with computation and applications of blockmodels. However, there is a surprising lack of attention to two very important aspects of blockmodel analyses: the interpretation and evaluation of the results. The purpose of this paper is to focus on these topics, primarily reviewing and synthesizing the approaches to interpretation and evaluation currently in use.

Predicting the structure of a communications network from recalled data

Abstract In a series of papers on informant accuracy in social network data, Bernard, Killworth, and more recently, Sailer, have concluded that “what people say, despite their presumed good intentions, bears no useful resemblance to their behavior” (Bernard, Killworth, and Sailer 1982: 63). In this paper we reanalyze one of the data sets (the technical group) utilized by Bernard, Killworth and Sailer in arriving at their conclusions. Unlike Bernard et al. we find that the observed behavior data corresponds closely to the recalled data. Using different methods of analysis we find that the verbal recall data can be used to predict structural aspects of the observed data. Two major findings emerge from our analysis: first, the more similarly two people judge the communication pattern of others, the more they interact with each other, and, second, the more two people share accurate knowledge of others, the more they interact with each other. Implications of our findings for the assertions of Bernard, Killworth and Sailer are discussed.

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

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.

Spatial arrangement of social and economic networks among villages in Nang Rong District, Thailand

Abstract This paper examines the spatial arrangement of social and economic networks among villages in Nang Rong district, Thailand. We use spatial information from a geographic information system (GIS) for the district to help interpret the patterns of movement of agricultural equipment (large tractors) between villages, of people into villages for temporary labor, and of people to village temples and to elementary and secondary schools within the district. Once social networks have been incorporated into the GIS they can be mapped in relation to geographic features of the district, such as topography, landcover, and locations of roads, rivers, and villages. Not only does geographic information about village locations allow us to properly orient the graphs of these networks, but the resulting visual displays reveal strikingly different spatial arrangements for the five networks. Networks of shared temples and elementary schools link small sets of villages in close geographic proximity whereas tractor hiring, labor movement, and secondary school networks bring together larger sets of villages and span longer distances. Information on landcover from satellite digital data provides insights into the patterns of network ties throughout the district and shows a clear relationship between tractor hiring networks and type of agricultural activity in the district. The spatial analytic capabilities of the GIS also allow us to assess the impact of the administratively defined district boundary on our measured relations and to evaluate whether rivers and perennial streams create barriers to network ties between villages.