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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]

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]

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 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]

The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a 'functorial' mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the 'theory of categories,' a branch of modem algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach. [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 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]

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]

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]

This paper presents a synthesis of the necessary and sufficient restrictions that insure a transitive group preference if majority rule is the aggregation procedure. We show the equivalence between transitivity and an extension of the condition of Condorcet which states that if an alternative receives a majority over every other, then it should be the social choice. This extension is equivalent to finding a solution to a system of linear inequalities. We use these inequalities to demonstrate that the recent work on restrictions of voter preferences can be derived from this Extended Condorcet Condition. [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]

A distinction is made between implicit and explicit group overlap in sociological data, and literature is briefly reviewed in terms of this distinction. The conclusion is drawn that for implicit overlap, the method of data analysis should use continuous input, while yielding output in a discrete form of (possibly overlapping) subsets. Such a method of clustering (ADCLUS) is presented briefly and is applied to the communication structure of a biomedical area of specialization. [ABSTRACT FROM AUTHOR]

Odds ratio (OR) and the educational Gini coefficient (EGINI) defined on a specific social grouping scheme can both be used to gauge educational inequality. In this study, we systematically review the scholarship that underpins the utilities of OR and EGINI and evaluate their properties across four research scenarios of allocating newly created opportunities under educational expansion. Formal analyses suggest that (1) both OR and EGINI monotonically increase (decrease) if the newly created educational positions are entirely delivered to the upper (lower) class. However, the rate of change differs between OR and EGINI. (2) When educational opportunities within expansion are allocated according to the relative populations of social classes, the probabilities of upper and lower classes to receive better education rise by the same extent, suggesting that all social classes benefit from the proliferation of educational credentials. This would drive down the EGINI, but change in OR is not monotonic. (3) EGINI remains unchanged if the newly created educational opportunities are allocated based on the initial class composition of better educated individuals before educational expansion. However, OR is driven to increase by the “Matthew Effect” where the increment in educational probability for the upper class is larger than that for the lower class. The discrepancy of empirical patterns between OR and EGINI is explained, and the practical implications are discussed using a case study of the educational policy evaluation in Britain. [ABSTRACT FROM PUBLISHER]

We show in this article that temporary bluffing has the power of promoting the transition from a bad to a good state in social systems. The analysis is carried out with reference to the simplest unit of interest in sociology—the couple—but it can be certainly extended to larger social groups. More precisely, an already available mathematical model shows that couples composed of so-called secure individuals with neither too high nor too low appeals have two alternative romantic regimes—one satisfactory and one not. Thus, if one of these couples is trapped in its unsatisfactory regime the problem is how to escape from that trap and switch to the satisfactory regime. Temporary bluffing, namely, giving to the partner for a sufficiently long time a biased impression of the involvement or of the appeal, is a very effective, though not unique, way for performing the switch. This, in a sense, attenuates the negative moral value usually given to bluffing in social behavior. [ABSTRACT FROM PUBLISHER]

In this article, we critically study whether social networks can explain the emergence of cooperative behavior. We carry out an extensive simulation program in which we study the most representative social dilemmas. For the Prisoner's Dilemma, it turns out that the emergence of cooperation is dependent on the microdynamics. On the other hand, network clustering mostly facilitates global cooperation in the Stag Hunt game, whereas degree heterogeneity promotes cooperation in Snowdrift dilemmas. Thus, social networks do not promote cooperation in general, because the macro-outcome is not robust under change of dynamics. Therefore, having specific applications of interest in mind is crucial to include the appropriate microdetails in a good model. [ABSTRACT FROM AUTHOR]

People often make choices or form opinions depending on the social relations they have, but they also choose their relations depending on their preferred behavior and their opinions. Most of the existing models of coevolution of networks and individual behavior assume that actors are homogeneous. In this article, we relax this assumption in a context in which actors try to coordinate their behavior with their partners. We investigate with a game-theoretic model whether social cohesion and coordination change when interests of actors are not perfectly aligned as compared to the homogeneous case. Using analytical and simulation methods we characterize the set of stable networks and examine the consequences of heterogeneity for social optimality and segregation in emerging networks. [ABSTRACT FROM AUTHOR]

This article examines the effects of status differentiation on the cohesion of a social structure, Using a formal model, we simulate the fates of a hypothetical cohort of newly hired employees, who are equals in the eyes of their boss and in the nascent stages of sorting into a status hierarchy. We cast these employees in a process in which they exert effort, receive public approval from the boss in exchange, and thus come to fill different places in a status order. We then consider the circumstances under which these workers cohere as a group and when, by contrast, differentiation makes cohesion among them unlikely. Our results show that the extent of the boss's autonomy in relationship to employees accounts for this difference in outcomes. Under an autonomous boss, as differentiation transpires, status-based social forces break the group of workers apart. Conversely, when the boss occupies a compromised position, group-level cohesion coexists with differentiation. Our main contribution is the intuition that the cohesion-related consequences of status differentiation can substantially depend on the tie between contestants and their external audience. We conclude by developing conjectures for empirical research consistent with our main findings. [ABSTRACT FROM AUTHOR]

Using dimes and pennies on a checkerboard, Schelling (1971, 1978) studied the link between residential preferences and segregational neighborhood patterns. While his approach clearly has methodological advantages in studying the dynamics of residential segregation, Schelling's checkerboard model has never been rigorously analyzed. We propose an extension of the Schelling model that incorporates economic variables. Using techniques recently developed in stochastic evolutionary game theory, we mathematically characterize the model's long-term dynamics. [ABSTRACT FROM AUTHOR]

French (1977), Harary (1959), and Abelson (1964) initiated a prominent line of social influence models to explain social norms or collective decisions from the structure of influence networks. These models fail to generate unstable decision dynamics, a phenomenon that can be observed in collective decision-making. To capture instability, we assume that decision-makers raise their level of salience to reduce expected losses from decision-outcomes. Our model generates persistently unstable outcome patterns under conditions related to the social network and to intolerance for expected losses. A 6-actor example reveals stable outcomes for low intolerance, complex oscillations for intermediate levels of intolerance, and simple and regular oscillation for high intolerance. We discuss implications for the predictability of collective decision-making. [ABSTRACT FROM AUTHOR]

We propose a structural approach to the representation of life history data, based on an interval graph formalism. Various "life history graphs" are defined using this approach, and properties of such graphs are related to life course concepts. The analysis of life history graphs using standard network methods is illustrated, and suggestions are made regarding the use of network analysis for life course research. A duality is demonstrated between individual life history graphs and social networks, and connections between life history graph analysis and conventional life course methods are discussed. [ABSTRACT FROM AUTHOR]

In general this comment tackles the problems and difficulties potentially combined with an application of formal economic models and constructs, such as the Walras equilibrium and microeconmic demand theory, to pure sociological contexts. In particular, this is done by analyzing a further attempt, as recently suggested by Braun (1993 and 1994), to extend the well-known Coleman Model by incorporating the embeddedness of social transactions in incomplete social network structures. "Pars pro toto" it is proved that Braun's conceptualization contains some weaknesses which imply that fundamental conclusions drawn in his article have to be revised. [ABSTRACT FROM AUTHOR]

The idea of partitioning a network in terms of a specific conceptualization of equivalence has taken a powerful hold on the imagination of network analysts. Frequently, an empirically established blockmodel is assessed in terms of its consistency with a particular visualization of a network. We demonstrate that, while a visual representation of a network can be helpful, this also constrains powerfully our image of the structure of that network. This implies that a particular picture of a network is not sufficient for establishing the adequacy of a blockmodel. We argue that once committed to a specific form of equivalence, a network analyst must be committed also to an explicit method of assessing the extent to which a blockmodel is consistent with the selected form of equivalence. We provide a method for doing this. Additionally, and perhaps more importantly, efforts to measure the fit of a blockmodel in terms of a sin- Sic form of equivalence reveal a serious weakness in the idea of using only a single form of equivalence to partition a network. It follows that this idea must be reconsidered. An appropriate generalization of the equivalence idea is one where each block, of a particular image in a blockmodel, is free to conform to a different form of equivalence. We provide a general criterion function, together with a local optimization procedure, for establishing such a generalized blockmodel. This criterion function also provides an appropriate measure of fit. Finally, we propose partitioning a network into a generalized blockmodel where each block, again in an image, can also have a particular pattern within which each equivalence type is a special case. Again, we provide a method for establishing such a model and assessing its fit. [ABSTRACT FROM AUTHOR]

The exchange networks that social psychologists have studied can usefully be represented as game theoretic 2-sided assignment games. Conceiving of these networks as 2-sided assignment games opens up the possibility of studying N-sided assignment games and games without cores. 2-sided assignment games are special in that they always have cores, stable solutions in which every individual and subgroup behave rationally. The implicit assignment of positions to categories of an N-sided assignment game is related to coloring a graph. The color classes form sets of positions with potentially related interests. Color equivalence is compared to structural, regular, automorphic, and ecological positional equivalence. [ABSTRACT FROM AUTHOR]

A new solution to the old problem of partitioning a matrix of social proximities into groups is proposed. It draws on a heuristic developed in computer science, the simple genetic algorithm. The algorithm is described and its utility is demonstrated with applications to three standard data sets. [ABSTRACT FROM AUTHOR]

The article focuses on the structure of communication network among actors and the personal trust induced by such a communication structure and its effects on the free rider problem. The concept of free rider is helpful to analyze many problems in modern societies where economic value dominates and privatizing freedom is expanding. One of the factors which makes actors select rationally free riding behavior is the rupture of communication among actors. If communication is possible, actors can get pieces of information about the attitudes of others, or have oral dealings, or establish trusting relationships between each other. Due to the rupture of communication, actors have no other way than selecting free riding behavior, even if there exists a far better situation in which all members could cooperate. As well know, J. S. Coleman's model is a free exchange market system where actors who have interests in some events exchange their control over events with others, being oriented to get control over events strongly interested in as possible as they can. The structure of system is determined by the interest and control matrix given. After the structure has been determined, there exists an equilibrium in the system where total demand and supply of control are balanced.

Equivalence has become a foundational concept in social network representations of social structure. Each use of an equivalence concept has two components: (i) the definition of equivalence and (ii) a computational algorithm for detecting equivalences, or the extent to which they exist. In all substantive contexts it is necessary to determine if a particular definition of equivalence is appropriate and the extent to which the computational algorithm faithfully mirrors the equivalence definition. An extensive comparison of structural equivalence, with two structural equivalence detectors, and regular equivalence, with one regular equivalence detector, is provided for a set of social structures. As blockmodels are, among other things, hypotheses about network structure, hypotheses about structure are used to obtain the networks used for these comparisons. For any network, there is, potentially, a multiplicity of equivalences that can be mobilized so as to complement each other in analyzing social structure. [ABSTRACT FROM AUTHOR]

The notion of "relative deprivation" as well as of "reference group" seems to be widely accepted among sociologists and social psychologists as one of significant concepts. However, there have been only few efforts to represent formally the mechanisms or processes where relative deprivation is generated. Sociologist R. Boudon has earlier attempted to formalize "the logic of frustration" within a game-theoretic framework as a case of what he calls perverse effects or unintended consequences of social action. Individuals behave more or less rationally trying to maximize their subjective expected utility; but as a consequence of aggregation of individual behavior, the end-result might be frustrating to them. Boudon constructs a simple model to capture such a situation, thereby to see implications of the phenomena generated by the model. The article aims firstly to follow Boudon's discussion and go a step further to see more precisely the implications of Boudon's model; secondly to see how well it captures various empirical episodes; and finally to modify a model from a non-stratified to a stratified society model, again according to Boudon's suggestion.

The article presents a discussion on the relationship between mathematics and social networks analysis. The latter is recognized as one of the fastest growing specialties in social science. Social networks analysis is based on traditions of different branches of subjects including anthropology, communications science, human geography, and information science. Mathematics has proved to be successful in research work in all the fields particularly physics. The subject focuses on the abstract structure or form of an argument. There are number of mathematicians who are well acquainted with the social networks area. There are several social scientists who are working in the networks area who know mathematics well.

A generalized model of diffusion of information in a closed, homogeneously mixing population of size N is considered. Apart from the provision of mass-mediated and interactively mediated messages and the possibility of spontaneous loss of interest, the model allows for the possibility of the process being stifled by a section of the people who possess the information but do not propagate it; they rather hinder the process by turning off the spreaders that come in their contact. The master equation for the model is set up and both deterministic and stochastic aspects of the stable, steady-state solution of the problem are analyzed. Existing models, such as the Kermack-McKendrick model, the Daley-Kendall model and the Bartholomew model, are retrieved as special cases. Several new features of the process emerging from our generalization are discussed and a special model displaying critical behavior is outlined. [ABSTRACT FROM AUTHOR]

A new approach to the understanding of sociological collective behaviour, based on the framework of critical phenomena in physics, is presented. The first step consists of constructing a simple mean-behaviour model and applying it to a strike process in a plant. The model comprises only a limited number of parameters characteristic of the plant considered and of the society. A dissatisfaction function is introduced with a basic principle stating that the stable state of the plant is a state which minimizes this function. It is found that the plant can be in one of two phases: the collective phase and the individual phase. These two phases are separated by a critical point, in the neighbourhood of which the system is very sensitive to small changes in the parameters. The collective phase includes a region of parameters for which the system has two possible states: a "work state" and a "strike state". The actual state of the system depends on the parameters and on the "history of the system." The irreversibility of the transition between these two states indicates the existence of metastable states. For these particular states, the effect of small groups of workers or of a small perturbation in the system results in drastic changes in the state of the plant. Other non-trivial implications of the model, as well as possible extensions and refinements of the approach, are discussed. [ABSTRACT FROM AUTHOR]

The concept of decisional power is introduced and compared with other measures for power like those of Shapley-Shubik, Banzhaf and Dahl. The sum of the powers of all actors in a social network is maximal for certain structures of the network. These structures are called completely democratic. Completely democratic structures are characterized. In every network dictator sets are present. These can be found by use of Boole polynomials. Decisional power turns out to have both a causal aspect and a utility aspect and to allow for variations that express the power over other persons as well as the power in a certain state of the network. [ABSTRACT FROM AUTHOR]

The effects of random environmental fluctuations on the process of diffusion of information in a social group are investigated. The methodology of this investigation is based on a study of "stochastic differential equations with fluctuating parameters," under the assumption that the time scale of the fluctuations in the various parameters is much shorter than that of the macroscopic variables of the system. This enables us to convert a stochastic differential equation into a Fokker-Planck equation which in turn can be solved for obtaining an explicit expression for the stationary state of the system. As an illustration, we analyze various cases of Bartholomew's model of diffusion of information in a randomly fluctuating environment and calculate the relevant statistical characteristics of interest. The resulting effects of environmental stochasticity on the process of diffusion of information are compared with the ones arising from the intrinsic stochasticity of the process, the latter depending inevitably on the size of the population group involved. [ABSTRACT FROM AUTHOR]

A fuzzy set theoretical framework is proposed for the analysis of sociometric structure characterized by vagueness of liking between individuals and a person's relative degree of belonging to a social group. Max-min transitivity of a fuzzy relation is employed as a basic concept to examine the degree of liking and clustering in group structures. A distance model based on min-max transitivity is also formulated as a special case of transitivity analysis. Other notions of transitivity such as the max-product and the max-* are also discussed. An empirical analysis is performed to examine the applicability of the proposed transitivity concepts. It appears that the current methodological construct provides a more appropriate perspective in the analysis of the group structure properties. [ABSTRACT FROM AUTHOR]

A model is considered for a situation in which two social groups compete with each other, ultimately resulting in the possible suppression of one of the groups. Using the method of system-size expansion, an asymptotic analysis of the model, including the time evolution of both deterministic and stochastic aspects of the process, is carried out. The probability distribution of the maximum size attained by the weaker group, just before the commencement of its decline, is examined and the results are compared with the previous work of Osei and Thompson on the "supersession of one rumour by another." The present model, which generalizes the Osei-Thompson model in a number of ways, is also relevant to the problems of opinion formation and attempted conversion of people from one viewpoint to another. [ABSTRACT FROM AUTHOR]

A societal network is defined to be a finite directed graph in which individuals are represented by nodes, and relations between individuals by labelled arcs. Each individual undergoes state transitions at discrete instants of time, so that the societal network may be thought of as a deterministic dynamic process. It is shown that the individuals of such a network may be divided into equivalance classes, so that the original network may be represented by a reduced network containing one node for each equivalence class. Similar results are obtained for a more general type of partition called a "class structure." The application of these concepts is illustrated in the context of "balanced" networks, which have either positive or negative relations between nodes. The longrun behavior of societal networks is then examined, and it is shown that any network will eventually reach either a stable state or a periodic pattern of state transitions. In the case of a probabilistic transition rule, it is proved that the long-run evolutionary pattern is independent of the initial state of the network. Finally, some potential areas of future work are suggested. [ABSTRACT FROM AUTHOR]

For any empirical structure consisting of a system S and its environment E, there is an associated digraph D whose points and arcs (directed lines) correspond to the elements and relationships of the structure. The arcs of D are thus of four types: (1) internal arcs, which join two points of S; (b) external arcs, which join two points of E; (c) out-liaisons of S, which join a point of S to one of E; and (d) in-liaisons of S, which join a point of E to one of S. The boundary of S is defined as the subgraph of D induced by the liaisons of S and corresponds to those elements and relationships of the structure directly involved in transactions between the system and its environment. The basic structural properties of boundaries are then identified, and it is shown how the points of S and E can be stratified according to their distances to (or from) the boundary of S. Next, several results are derived concerning system-environment relationships in structures whose digraphs are symmetric, transitive, or signed. The concept of convexity is then introduced to deal with a certain kind of segregation of a system relative to its environment. And, finally, it is shown how the adjacency matrix of D can be employed to facilitate the analysis of such structures and the calculation of various indexes of system-environment relationships. [ABSTRACT FROM AUTHOR]

The conceptual and mathematical framework of a general model for distance within sociometric structure is described. The model characterizes "balance" in terms of the triangle inequality, in which the distance between two people (A and C) should be less than or equal to the sum of the distances to a third person (B) , i.e., d(A,C) ≤ d(A,B) + d(B,C). The notion of addition of distances is developed. Different ways of adding distances result in different models of sociometric structure. Two families of models for symmetric graphs are discussed. The general model is extended to asymmetric graphs by generalizing the notion of transitivity. The model's potential for resolving a problem of the transitivity model is then discussed. The general model provides a means of examining the relationship between stratification and clustering in the structure of groups. [ABSTRACT FROM AUTHOR]

Berger has developed a standard experimental situation for the study of influence processes in dyads. A simple model is presented which orders the empirical results of eight experiments (27 conditions) on status-undifferentiated dyads in this situation. The model provides a good fit to the data and makes additional predictions. [ABSTRACT FROM AUTHOR]

Both functionalism and exchange theory presuppose the existence of a worth ordering of some sort enabling members of a group to evaluate contributions to the group. Thus it is possible for participants to tell which of two patterns of behavior is more functional, or whether or not two social gifts are equivalent etc. Statements by earlier authors regarding this worth ordering are examined. It is shown that they imply that associated with any social group there exists a non-arbitrary set of exchange ratios (social prices) between various social actions. These social prices can be used to evaluate the contributions of individuals to the group and to determine the rankings of individuals within the group. [ABSTRACT FROM AUTHOR]

Inverse semigroups are introduced as a model for kinship structures. It is shown that semigroups are implied by the traditional anthropological law of uniform descent, and that inverses are suggested by the principle of reciprocity. A separation into a 'surface' and a 'deep' level of analysis was induced by viewing a kinship system as a partition on an underlying inverse semigroup. Some Omaha-type kinship systems are decomposed into direct and semidirect products. Additional assumptions are made to derive a theoretical similarity measure, which is then compared with a judged similarity task on Tenejapan Indians. The results of this preliminary experiment seem to he encouraging. [ABSTRACT FROM AUTHOR]

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non-random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choicest One model is a simulation in which individual members of two recognizable coups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to `neighborhood tipping? The systemic effects are found, to be overwhelming; there is no simple correspondence of individual incentive to collective results, Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of `tipping' begins to emerge. [ABSTRACT FROM AUTHOR]