ABSTRACT: In the last fifteen years, ecosystem ecologists have developed a theoretical approach and a set of computational methods called “ecological network analysis” (Ulanowicz, 1986; Kay et al. 1996). Ecological network analysis is based on input/output models of energy or material flows (e.g., carbon compound flows) through a trophic network (e.g., a food web describing which species eats which other species). Mathematically and conceptually, this ecological network analysis approach is strikingly similar to work in the field of social network analysis, particularly the influence models of Hubbell (1965), Katz (1963), and Friedkin and Johnsen (1990). In food web research, Yodzis and Winemiller (1999), have recently proposed a new way to operationalize the concept of a "trophospecies", which is a set of species with similar foods or predators. Their definition turns out to be identical to the notion of structural equivalence (Lorrain and White, 1971) in social network analysis, particularly as conceived by Burt (1976) and Burt and Talmud (1993). The striking convergence to date of the fields of ecology and sociology via independent invention of network concepts suggests that there may be considerable value in cross-fertilization of the two fields. With this paper we hope to begin a dialogue between the two fields, by applying advanced social role theory and methods to the study of food webs. In social network analysis, the introduction of the notion of structural equivalence thirty years ago was followed by the development of regular coloration (White & Reitz, 1983; Everett & Borgatti, 1991), an important advance over structural equivalence for modeling social roles. The objective of our paper is to answer a call in the ecological literature for greater clarity in thinking about the role of species in ecosystems (Simberloff and Dayan, 1991), by applying the notion of regular coloration to food webs.
ABSTRACT: This paper contributes to an ongoing debate in International Political Economy about the appropriateness of globalization, regionalization and macroeconomic imbalance theory by identifying quantitative estimates for all three tendencies from world trade data. This is achieved with a series of gravity models enhanced stepwise by the mapping of the estimation errors of a given model on representations of the overall structure of trade. This not only allows the identification of imperfections in a given model but also permits the further improvement of the models since any systematic regional organization in the error-terms can be identified. The results of the most elaborated model indicate that single factor explanations of global economic integration are presumably misleading. Instead, each of three explanations captures only part of the ongoing changes, as they can be identified under a comparative static perspective from world trade data.
ABSTRACT: The research we report here tests the "Freeman-Linton Hypothesis" which we take as arguing that the structure of a set of relational ties over a population is more strongly determined by type of relation than it is by the type of species from which the population is drawn. Testing this hypothesis requires characterizing networks in terms of the structural properties they exhibit and comparing networks based on these properties. We introduce the idea of a structural signature to refer to the profile of effects of a set of structural properties used to characterize a network. We use methodology described in Faust and Skvoretz (forthcoming) for comparing networks from diverse settings, including different animal species, relational contents, and sizes of the communities involved. Our empirical base consists of 80 networks from three kinds of species (humans, non-human primates, non-primate mammals) and covering distinct types of relations such as influence, grooming, and agonistic encounters. The methods we use allow us to scale networks according to the degree of similarity in their structuring and then to identify sources of their similarities. Our work counts as a replication of a previous study that outlined the general methodology. However, as compared to the previous study, the current one finds less support for the Freeman-Linton Hypothesis.
ABSTRACT: This paper is about estimating the parameters of the exponential random graph model, also known as the p* model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or Metropolis-Hastings sampling. The estimation procedures considered are based on the Robbins-Monro algorithm for approximating a solution to the likelihood equation.
A major problem with exponential random graph models resides in the fact that such models can have, for certain parameter values, bimodal (or multimodal) distributions for the sufficient statistics such as the number of ties. The bimodality of the exponential graph distribution for certain parameter values seems a severe limitation to its practical usefulness.
The possibility of bi- or multimodality is reflected in the possibility that the outcome space is divided into two (or more) regions such that the more usual type of MCMC algorithms, updating only single relations, dyads, or triplets, have extremely long sojourn times within such regions, and a negligible probability to move from one region to another. In such situations, convergence to the target distribution is extremely slow. To be useful, MCMC algorithms must be able to make transitions from a given graph to a very different graph. It is proposed to include transitions to the graph complement as updating steps to improve the speed of convergence to the target distribution. Estimation procedures implementing these ideas work satisfactorily for some data sets and model specifications, but not for all.
ABSTRACT: Most personal (egocentric) network studies describe networks using measures that are not structural, opting instead for attribute-based analyses that summarize the relationships of the respondent to network members. Those researchers that have used structural measures have done so on networks of less than 10 members who represent the network core. Although much has been learned by focusing on attribute-based analyses of personal network data, the application of structural analyses that are traditionally used on whole (sociocentric) network data may prove fruitful. The utility of this approach becomes apparent when the sample of network members elicited is relatively large.
Forty-six respondents free-listed 60 network members and evaluated tie strength between all 1,770 unique pairs of members. Graph-based measures of cohesion and subgroups revealed variability in the personal network structure. Non-hierarchical clustering generated subgroups that were subsequently verified by respondents as meaningful. Further analysis of the correlation between subgroup types and overlap between subgroups demonstrates how the analysis of each network can be summarized across subjects. Four case studies are presented to illustrate the richness of the data and the value of contrasting individual matrix results to the norm as defined by all 45 subjects.
ABSTRACT: Networks of exchange opportunities can evolve as dissatisfied agents search for new partners. Are there stable networks whose participants do not look for new potential partners? What do these networks look like? How is the outcome of this evolutionary process related to the beginning network? Computer simulations are used to explore how networks of exchange opportunities evolve when agents can change positions. These simulations suggest that only networks with high degrees of power imbalance are unstable and that there are three forms for stable networks: equal power, indeterminate power, and inconsistent power (corelessnesss).
ABSTRACT: We propose a novel visualization approach that facilitates graphical exploration and communication of relative actor status in social networks. The main idea is to map, in a drawing of the entire network, actor status scores to vertical coordinates. The resulting problem of determining horizontal positions of actors and routing of connecting lines such that the overall layout is readable is algorithmically difficult, yet well-studied in the literature on graph drawing. We outline a customized approach. The advantages of our method are illustrated in a study of policy making structures from the privatization processes of former East German industrial conglomerates, in which the visual approach led to additional findings that are unlikely to have been revealed using non-visual means of analysis.
ABSTRACT: In the last fifteen years, ecosystem ecologists have developed a theoretical approach and a set of computational methods called “ecological network analysis” (Ulanowicz, 1986; Kay et al. 1996). Ecological network analysis is based on input/output models of energy or material flows (e.g., carbon compound flows) through a trophic network (e.g., a food web describing which species eats which other species). Mathematically and conceptually, this ecological network analysis approach is strikingly similar to work in the field of social network analysis, particularly the influence models of Hubbell (1965), Katz (1963), and Friedkin and Johnsen (1990). In food web research, Yodzis and Winemiller (1999), have recently proposed a new way to operationalize the concept of a "trophospecies", which is a set of species with similar foods or predators. Their definition turns out to be identical to the notion of structural equivalence (Lorrain and White, 1971) in social network analysis, particularly as conceived by Burt (1976) and Burt and Talmud (1993). The striking convergence to date of the fields of ecology and sociology via independent invention of network concepts suggests that there may be considerable value in cross-fertilization of the two fields. With this paper we hope to begin a dialogue between the two fields, by applying advanced social role theory and methods to the study of food webs. In social network analysis, the introduction of the notion of structural equivalence thirty years ago was followed by the development of regular coloration (White & Reitz, 1983; Everett & Borgatti, 1991), an important advance over structural equivalence for modeling social roles. The objective of our paper is to answer a call in the ecological literature for greater clarity in thinking about the role of species in ecosystems (Simberloff and Dayan, 1991), by applying the notion of regular coloration to food webs.
ABSTRACT: This chapter discusses theoretical sociology in historical perspective: From the classic tradition to postclassical efforts of synthesis that culminated in multiple paradigms, to the situation today in which theorists are more and more constructing formal models as essential components of their methodology. The classical phase is treated very briefly and the discussion of the postclassical phase is limited to two major theorists, Parsons and Homans, in terms of their common focus on the Durkheimian problem of social integration. The bulk of the chapter deals with developments in recent theoretical sociology. I describe models of structure and of process before defining two types of models that combine a structural focus with process analysis. Finally, I set out a general perspective on theoretical model building and conclude with a discussion of standards in the assessment of such work.
ABSTRACT: This paper examines the degree to which the constraints imposed by various social contexts influence social interaction. We draw on two data sets. In each, we compare the patterning of interaction of the same individuals across different contexts. If minimal constraints are imposed, then the interaction patterns among the individuals in the two contexts should be similar. But if one of the contexts involves major constraints, then interaction patterns in the two should differ. The results suggest further that the constraints found in any context are not unlimited in their impact. Moreover, individuals who can, apparently do manipulate the context to minimize the constraint imposed by the context.
ABSTRACT: Data structures comprising many binary variables can be represented graphically in various ways. Depending on the purpose different plots might be useful. Here two ways of showing associations between variables and implications between variables are discussed. The methods are based on conditional independence graphs and lattices of maximal cluster-property pairs. Applications to multivariate samples and network data are briefly discussed.
ABSTRACT: In this article, we discuss the concept of social integration and its implications for health. We provide both an overview of the social epidemiology and a review of theories of how participation in a diverse social network might influence health. We also present evidence from a prospective study of social network diversity (number of social roles) and susceptibility to the common cold in people experimentally exposed to a cold virus. We found that the greater the social diversity, the lesser the susceptibility to infectious illness. However, our attempts to isolate the pathways through which social diversity was associated with susceptibility (health practices, hormones, immune function) were unsuccessful. The relation was independent of the number of people in the social network, and of personality characteristics thought to influence social participation.
ABSTRACT: We present an overview of eigen analysis methods and their applications to network analysis. We consider several network analysis programs/procedures (Correspondence Analysis, NEGOPY, CONCOR, CONVAR, Bonacich centrality) that are at their core eigendecomposition methods. We discuss the various matrix representations of networks used by these procedures and we give particular attention to a variety of centering and normalizing procedures that are carried out prior to the analysis. We compare three types of iterative procedures with the standard SVD in terms of pragmatic concerns and the results produced by each method. We show how the initial matrix representations and the adjustments made between iterations influence the results obtained. Finally, we show that the eigen perspective clearly highlights the similarities and differences between different network analysis procedures.
ABSTRACT: This paper documents the use of pictorial images in social network analysis. It shows that such images are critical both in helping investigators to understand network data and to communicate that understanding to others.
The paper reviews the long history of image use in the field. It begins with illustrations of the earliest hand-drawn images in which points were placed by using ad hoc rules. It examines the development of systematic procedures for locating points. It goes on to discuss how computers have been used to actually produce drawings of networks, both for printing and for display on computer screens. Finally, it illustrates some of the newest procedures for producing web-based pictures that allow viewers to interact with the network data and to explore their structural properties.
John Skvoretz, Editor