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Correspondence analysis, a data analytic technique used to study two-way cross-classifications, is applied to social relational data. Such data are frequently termed sociometric or network data. The method allows one to model forms of relational data and types of empirical relationships not easily analyzed using either standard social network methods or common scaling or clustering techniques. In particular, correspondence analysis allows one to model: -two-mode networks (rows and columns of a sociomatrix refer to different objects) -valued relations (e.g. counts, ratings, or frequencies). In general, the technique provides scale values for row and column units, visual presentation of relationships among rows and columns, and criteria for assessing dimensionality or graphical complexity of the data and goodness-of-fit to particular models. Correspondence analysis has recently been the subject of research by Goodman, Haberman, and Gilula, who have termed their approach to the problem canonical analysis to reflect its similarity to canonical correlation analysis of continuous multivariate data. This generalization links the technique to more standard categorical data analysis models, and provides a much-needed statistical justification. We review both correspondence and canonical analysis, and present these ideas by analyzing relational data on the 1980 monetary donations from corporations to nonprofit organizations in the Minneapolis-St. Paul metropolitan area. We also show how these techniques are related to dyadic independence models, first introduced by Holland, Leinhardt, Fienberg, and Wasserman in the early 1980s. The highlight of this paper is the relationship between correspondence and canonical analysis, and these dyadic independence models, which are designed specifically for relational data. The paper concludes with a discussion of this relationship, and some data [ABSTRACT FROM AUTHOR]

This paper investigates bandwagon dynamics in social networks, using an extension of Granovetter's (1978) threshold model. The focus is on the pattern of social ties connecting actors with different participation thresholds. A benchmark model, in which actors' thresholds are similar to their neighbors' thresholds, is built from the principle of homophily. Computational experiments show that participation levels increase when network structure departs from pure homophily, such that actors have new neighbors with discrepant thresholds. Further increasing the heterogeneity of network neighbors causes the bandwagon effects to wane, however, suggesting that bandwagon dynamics are maximized when there is a balance of heterogeneity and homogeneity in social networks. This principle is consistent with insights from several empirical studies and consistent with the conclusions of other formal models. [ABSTRACT FROM AUTHOR]

In this paper we both describe and analyze the meeting process and the evolution of a friendship network among sociology freshmen in the Netherlands. We develop a theory that explains how changes in the network structure depend on one or more of four main effects; proximity, visible similarity, invisible similarity, and network opportunity. We formulate expectations with regard to what factors are important at what stages of the friendship development, making a distinction between 'meeting' and 'mating.' To some extent, the results confirm our expectations. The proximity and visible similarity variables determine change in network structure in the early stages, whereas network opportunity is important during all stages. Unfortunately, no significant effects of invisible similarity are found. [ABSTRACT FROM AUTHOR]

This paper extends the standard network centrality measures of degree, closeness and betweenness to apply to groups and classes as well as individuals. The group centrality measures will enable researchers to answer such questions as `how central is the engineering department in the informal influence network of this company?' or `among middle managers in a given organization, which are more central, the men or the women?' With these measures we can also solve the inverse problem: given the network of ties among organization members, how can we form a team that is maximally central? The measures are illustrated using two classic network data sets. We also formalize a measure of group centrality efficiency, which indicates the extent to which a group's centrality is principally due to a small subset of its members. [ABSTRACT FROM AUTHOR]

This paper addresses the development of a semigroup model of social networks. Data matrices which represent the perceived relationships between members of a social network are used to construct a (possibly infinite) data semigroup of derived relations defined by (real) matrix multiplication. This complex structure is analyzed by forming interaction semigroups. These semigroups are homomorphic images of the data semigroup. The corresponding congruences are generated by identifying products of finite order which are highly positively correlated. Several methods of generating the interaction semigroups are examined and are shown to generate nonhomomorphic semigroups. For each congruence, an associated triple of numbers can be defined which may serve as an indicator of the validity and/or a measure of the stability of the semigroup model. A series of hypothetical examples is developed to study how the algebraic properties of interaction semigroups reflect and uncover properties of associated networks. Specifically, relationships between homogeneity of a network and the algebraic structure of the corresponding interaction semigroup are addressed. The applicability of the above techniques to blockmodels is demonstrated. [ABSTRACT FROM AUTHOR]

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points In this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions. In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor. Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept. Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their "best" requests and learn by experience. We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to "bolster" their own preference as much as possible. We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models. [ABSTRACT FROM AUTHOR]

Friendship networks usually show a certain degree or segmentation: subgroups of friends. The explanation of the emergence of such groups from initially dyadic pair friendships is a difficult but important problem. In this paper we attempt to provide a first contribution to the explanation of subgroup formation in friendship networks by using the LS set as a definition for a friendship group. We construct a dynamic individual oriented model of friendship formation and provide preliminary simulation results that give an idea of how to continue the process of explaining group formation. [ABSTRACT FROM AUTHOR]

This paper examines the usefulness for theoretical work of the narrative method proposed by Peter Abell. Our assessment proceeds by using the narrative method to perform the two main tasks of theoretical analysis--constructing postulates and deriving predictions. To illustrate, we focus on the theory of distributive justice and the more general theory of comparison processes to which it led. The results of our assessment of the usefulness of Abell's narrative method for theoretical work indicate that the narrative method has far wider applicability than Abell has claimed for it. For example, (i) it is useful for all theoretical work in the sociobehavioral sciences, not only for theoretical work based on game theory, (ii) it is useful for analyzing thought-experiments as well as narrative accounts of actual actions and events, and (iii) the events in the narrative need not be restricted to human actions but can include events not traceable to human agency. We conclude also that Abell's narrative method complements the use of mathematical analysis in theoretical work and that it may be especially valuable for theoretical derivation involving two or more theories jointly. [ABSTRACT FROM AUTHOR]

This paper concerns the dynamical interactions between the macro structures of a society. From three axioms governing social interaction, a combined cooperative-competitive model consisting of a nonlinear differential system of equations is introduced. Various social and political phenomena are interpreted through the parameters (also called strategies) of the model, including coalitions, alliances, and revolutions. For example, four distinct types of revolutions can be identified. Questions of existence, uniqueness, and asymptotic stability of equilibria are answered. A striking feature of the model is that, in the constant parameter case, stability is assured, thus illustrating that social power and control systems change only when external or internal changes on the system parameters are imposed. These results are applied to alliances and revolutions with a focus on changes in the equilibria as determined by changes in the system parameters. [ABSTRACT FROM AUTHOR]

This paper argues that parties and other gatherings are important for the development of friendship networks. It proposes a stochastic model for the evolution of networks over time, the distinctive feature of which is the party event. A party event occurs when a person in the network has a gathering and invites all of his/her friends who then also become friends. The Party Models discussed are all based upon this simple assumption. After formulating basic assumptions, various differential equations describing Party Models are derived. Subsequently several concepts useful for model analysis are defined and briefly explored. These include the concepts of potential, equivalence class form, and degenerate models. The penultimate section considers models for three person networks in some detail and with numerical illustrations. All extended mathematical arguments are placed in the Mathematical Appendix. [ABSTRACT FROM AUTHOR]

This paper uses the concept of the triad census as developed by Holland and Leinhardt, and describes several distributions on directed graphs. Methods are presented for calculating the mean and the covariance matrix of the triad census for the uniform distribution that conditions on the number of choices made by each individual in the social network. Several complex distributions on digraphs are approximated, and an application of these methods to a sociogram is given. [ABSTRACT FROM AUTHOR]

In this paper, the equilibrium properties of Coleman's (1973) model of social exchange are explored as a prelude to making interpretations about the dynamics implicit in static models of exchange in general, this model in particular. The model is first presented in the conventional way--as an exchange condition embedded within more general equilibrium conditions, and the subsequent analysis of the model is enriched by examining its equilibrium at aggregate as well as disaggregate levels and by interpreting the model as a set of flows or networks. Its equilibrium properties are then described. First, it is shown how a model in which the exchange condition is a function of its equilibrium, defines an equilibrium which is reproducible and reversible in the stochastic sense. Tests for reversibility are given which show how the equilibrium conditions can be computed from inspection of the data set. Second, an underlying flow structure to the model is assumed, and it is shown how equilibrium in this structure is equivalent to the exchange condition being met. This produces symmetric flows or equal exchange at the aggregate level and a reversible equilibrium. The real interest in this analysis is on how near an actual system is to such equilibria and thus a set of accounts measuring such departures from equilibrium in terms of aggregate and disaggregate flows is presented. Finally, a test example based on the data used by Michener, Cohen and Sorensen (1977) is presented to illustrate the concepts of proximity to structural and reversible equilibria. [ABSTRACT FROM AUTHOR]

Our status-related behavior toward others is a function of the characteristics we perceive them to possess. Expectation states theory specifies the nature of the relationship between social characteristics and behavior, but until recently was limited to situations in which only one characteristic is perceived. This paper adds to the theory additional general assumptions from which an information-combining model is derived. This model specifies status-related behavior in multiple characteristic situations and other circumstances beyond the original scope of the theory. Comparisons of the model with other formulations provide excellent support. [ABSTRACT FROM AUTHOR]