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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]

All agree that many factors contribute to ethnic segregation, but controversy continues regarding the relevance of particular factors. In my paper I acknowledge the importance of discrimination, but I direct attention to the role of ethnic preferences and social distance dynamics. I do so because many dismiss the relevance of these factors for contemporary segregation without engaging formal theories and analytic models which suggest that dynamics associated with in-group attraction and out-group avoidance may take on increasing importance as past forms of discrimination slowly fade. Agent-based modeling shows promise for exploring the issue of whether prejudice against out-groups and affinity toward in-groups can build and sustain segregation in the absence of discrimination. Research drawing on this approach is at an early stage of development but is significant for highlighting two things. One is that the implications of preferences for segregation are strongly conditioned by the ethnic demography of the city. Another, closely tied to the first, is that different views about the implications of preferences for segregation often hinge on inconsistencies in how notions of integration and segregation are applied in discussions of individual location choices, the ethnic mix of single neighborhoods, and the ethnic distributions for all neighborhoods in a city. Critiques of agent-based models of Schelling-style preference effects will carry more force when they outline models indicating how location decisions guided by preferences documented in surveys can produce or sustain integration. [ABSTRACT FROM AUTHOR]

We consider social networks in which the relations between actors are governed by latent classes of actors with similar relational structure, i.e., blockmodeling. In Snijders and Nowicki (1997) and Nowicki and Snijders (2001), a Bayesian approach to blockmodels is presented, where the probability of a relation between two actors depends only on the classes to which the actors belong but is independent of the actors. When actors are a priori partitioned into subsets based on actor auributes such as race, sex and income, the model proposed by Nowicki and Snijders completely ignores this extra piece of information. In this paper, a blockmodel that is a simple extension of their model is proposed specifically for such data. The class affiliation probabilities are modeled conditional on the actor attributes via a multinomial probit model. Posterior distributions of the model parameters, and predictive posterior distributions of the class affiliation probabilities are computed by using a straightforward Gibbs sampling algorithm. Applications are illustrated with analysis on real and simulated data sets. [ABSTRACT FROM AUTHOR]

Researchers have identified several problems in measuring the strongest path connecting pairs of actors in valued graphs. To address these problems, it has been proposed that average path value be used to indicate optimal connections between dyads. However, a lack of proper computer algorithm and its implementation has hindered a wide-range application of the proposed solution. In this paper we develop a computer algorithm and fully implement it with four JAVA programs, which are available on request. These programs produce an optimal connection matrix, which is subsequently inputted into UCINET for further multidimensional scaling and clustering analysis. We demonstrate this procedure with a data matrix containing 38 organizations in information technology. We discuss the methodological implications of the application of our algorithm to future social network studies. [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 studies the optimal State support policy for an economy of retailers in which there is a criminal organization (called the Gang) that tries to enforce a rake-off scheme via punishment of reluctant retailers. The State aims at reducing the cost of reluctance through a suitable support policy (protection and insurance against physical damage) in order to undermine the Gang's threatening power and eventually to defeat it. Optimal support policies are determined for various rake-off schemes under the assumption that retailers tend to abandon expensive strategies for cheaper ones. [ABSTRACT FROM AUTHOR]

Three-way social network data occurs when every actor in a social network generates a digraph of the entire network. This paper presents a statistical model based on cultural consensus analysis for aggregating these separate digraphs into a single consensus digraph. In addition, the model allows estimation of separate hit and false alarm rates for each actor that can vary within each actor in different regions of the digraph. Several standard signal detection models are used to interpret the hit and false alarm parameters in terms of knowledge and response bias. A published three-way data set by Kumbasar, Romney, and Batchelder (American Journal of Sociology, 1994) is analyzed, and the model reveals that both response bias and knowledge decrease with distance from ego. [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]

This paper describes the central-union theory, which offers a new approach to the formation of coalition structures in cooperative, sidepayment, superadditive n-person games. This theory treats formation of coalition structures as a probabilistic, endogenous process. Fundamental to this process is the new concept of coalition structure candidate set. For any given coalition structure, the predicted probability of formation is a function of two variables: (1) whether the coalition structure is a member of the coalition structure candidate set (coalition structures not in the candidate set will not form) and (2) the extent to which players accept that coalition structure. Players' acceptance, in turn, depends on differences among players in the level of satisfaction regarding the allocation of payoffs within the coalition structure. [ABSTRACT FROM AUTHOR]

In the paper four semirings for solving social networks problems are constructed. The closures of the matrix of a given signed graph over balance and cluster semirings can be used to decide whether the graph is balanced or clusterable. The closure of relational matrix over geodetic semirings contains for every pair of vertices u and v the length and the number of u - v geodesics; and for geosetic semiring the length and the set of vertices on u - v geodesics. The algorithms for computing the geodetic and the geosetic closure matrix are also given. [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 fields of study from cognition to organizations and social networks, empirical structures have been formally represented in terms of graph theoretical models. When the empirical relationships can be seen as valued, a valued graph or digraph is called for. Values have been conventionally identified with real numbers, but other sorts of entities (most often signs) have been used. In this paper, we demonstrate a general system under which graphs and digraphs with values that are not numbers may be used to represent various important properties and features of empirical structures. Special cases include multiplexity of relationships, formal and informal linkages in organizational structures, systems and their environments, and structural consistency principles. The general system incorporates a matrix methodology which permits the convenient analysis of empirical structures. These cases are also intended to exemplify the ways in which valued relational models may be developed to extend this kind of formalization and its methodology to other areas of substantive interest. [ABSTRACT FROM AUTHOR]

Boyle has given a condition for defining a homomorphism in terms of minimal paths for undirected graphs. The purpose of such homomorphisms is to provide a simpler graph which will reflect the structure of the more complex graph, and thereby enable the researcher to make observations which may have been shrouded by a preponderance of nodes and edges. This paper develops Boyle's ideas and introduces further homomorphisms for directed as well as undirected graphs. The relationships between the various homomorphisms are also examined. [ABSTRACT FROM AUTHOR]

This paper presents a model of change in sociometric structure in an idealized "small" group where everyone is in constant, uniform interaction. After the model is discussed dynamically, the set of invariant sociograms for this model is defined and compared to those defined for other theories. The model is shown to include the strong forms of balance theory, clustering, transitivity, and positive balance. The model predicts that the weak forms become strong forms under constant contact. Equilibrium conditions are discussed in some detail, and specific examples are displayed, including examples which are not predicted by balance theory, clustering, or other theories. [ABSTRACT FROM AUTHOR]