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Although there has been much discussion in recent years of the applicability of mathematical methods in the social sciences, little attention has been paid to the interaction of the sociological analysis and the mathematics. In this paper, an example of an extremely fruitful interaction between anthropology and mathematics is described. The interaction has, on the one hand, greatly increased the subtlety and sophistication of the sociological analysis, while on the other hand it has posed interesting mathematical questions. [ABSTRACT FROM AUTHOR]

This paper presents a generalization of the concept of "structural equivalence ", the key concept in algebraic approaches to the study of social networks. Two points in a graph or set of relations will be called "structurally related" if they are connected in the same ways to structurally related points. It is suggested that this new definition suitably weakens Lorrain and White's categorical approach, and is more appropriate than CONCOR. Structural relatedness is compared to these approaches via several simple examples. [ABSTRACT FROM AUTHOR]

This paper is an attempt to examine and define the world network of a typical individual by discovering how many of his or her acquaintances could be used as first steps in a small-world procedure, and for what reasons. The town and occupation of each target was provided, together with the ethnic background, where this could not be inferred from the name. Starters were instructed in the small-world experiment and asked to write down their choice, amongst the people they knew, for the first link in a potential chain from them to each of 1267 targets. Starters provided information on each choice made (e.g. mother, cousin, friend, acquaintance, etc.) together with the sex of the choice) and the reason that choice had been made. The reason could be in one or more of four categories: something about the location of the target caused tile starter to think of his or her choice; the occupation of the target was responsible for the choice; the ethnicity of the target; or some other, unspecified, reason. Six main conclusions may be drawn from the data: (1) A mean of 210 choices per starter account for the "world" (i.e. the 1267 targets). This number is probably an underestimate. Only 35 choices are necessary to account for half the world, however, Of the 210, 95 (45%) were chosen most often for location reasons, 99 (4 7%) were chosen most often for occupation reasons, and only 7% of the chokes were mainly based on ethnicity or other reasons. (2) Chokes were mainly friends and acquaintances, with strong cleavage by sex. For any given target, the type of choke used by the majority of starters was a friend or acquaintance, and not family. For any given target, the most likely sex of the choice (i.e. over all starters) can be predicted accurately on 82% of occasions. This sex tends to be male, unless both starter and target are female, or if the target has a low-status occupation. Additionally, any given starter is most likely to pick a male choice for any target, except for the female starter-female target combination, when female choices are more likely. This was correct on 64% of occasions. (3) Location was the usual reason for choice (out of the four categories), with occupation second, and ethnicity or other reasons rarely used. This most popular reason for choice may be correctly predicted for any given target 81% of the time. (4) The decision as to which choke was made appears to depend primarily on the occupation of the target, and secondly on the distance (near/far) from Morgan town, West Virginia, where the experiment took place. (5) The expression "having one's man in ..." can be partially quantified. We may define a choke to "handle" a state in the U.S. if he or she was chosen for two-thirds or more of the targets in that state for which choices were made on the basis of location. Then, for any starter, on average, half the states are each handled by a single choice. (6) The accuracy of starters' recall about their networks is low, in the sense that their recall is incorrect more often than it is correct (i.e. their recall could not be put to any other use with any reliability). This confirms previous experiments on informant accuracy. [ABSTRACT FROM AUTHOR]

This paper poses two questions about the process of friendship formation: what is the relative stability of asymmetric and mutual friendship dyads and what is the nature of change in asymmetric dyads over time? These questions are examined in longitudinal sociometric data from five elementary classes. Change in friendship choices is shown to be at least partially embeddable as a continuous time, stationary Markov process and the unique Q matrices governing the process are determined. The findings show that unreciprocated friendship choices of the children in the sample are less stable than reciprocated choices and that their unreciprocated choices tend to be withdrawn rather than reciprocated over time. [ABSTRACT FROM AUTHOR]

Corporate networks studies have been restricted mainly to the private or business sectors. Network analyses involving both corporations and state or government agencies have been extremely rare. In this paper, the inter- corporate network of interlocking directorates in the Netherlands, based on 86 large corporations and financial institutions, is studied in terms of a bi- partite corporate-governmental network which arises from the interlocking memberships linking these corporations with major committees, agencies and similar centers of decision in the public sector or central state mechanisms in the Netherlands. The corporations, representing 27 industrial sectors, have been related to government and state agencies in 28 policy sectors. In this exploratory analysis the two heavy industries, metal/shipbuilding and chemicals/oil stand out clearly. With respect to the 17 central firms the results demonstrate consistent correspondence between their central position in the Dutch corporate network and the degree of their interlocks with policy sectors in the state. The results also show that the interlocks are overwhelmingly linked with the two policy sectors "economic affairs" and "education and sciences". Hence a more detailed analysis of the interlocks with these two policy sectors is reported. [ABSTRACT FROM AUTHOR]

Recent work on economic structure has tended to focus around discovering general or global mappings to represent complex patterns of binary or multiplex ties. By contrast, this paper seeks to define an intermediate level of structure-the "enterprise "-and to measure it concretely using a combination of ownership and director/officer ship or executive board membership ties. In the first section, we outline the theoretical and substantive basis of the concept of "enterprises" as it is used in the literature. Difficulties in the operationalization of this concept are then surveyed and some tentative solutions suggested. In the second section, we describe in detail the methods used to implement our definition of enterprises for a set which includes the 5306 firms which most directly shape the Canadian economy. The third section outlines the impact of the use of four slightly different versions of this definition on arrays of enterprise memberships. Finally, the larger implications of our findings-both for the measurement of intermediate levels of structure and for the study of cross-national economic connections-are discussed. [ABSTRACT FROM AUTHOR]

This paper provides a comparison of the triadic-level structure inherent in behavioral and cognitive social network data taken on the same group, using a variety of groups whose communication could easily be monitored. It is found that many types of structure occur significantly more or less than chance in both behavioral and cognitive data, and providing that these are treated in similar ways, there is good agreement between the two structures. However, there are several ways to treat behavioral data, and these produce at least two essentially different structures. If cognitive and behavioral triads are compared, triad by triad, then there is virtually no agreement between them (even though they may both display the same structure on an overall triad census). Finally, as a demonstration of the dangers of relying solely on cognitive data, an unlikely null hypothesis is proposed. This asserts - for demonstration purposes - that, under many circumstances, behavioral structure never alters. Change in structure over time apparently occurs because of informant error in the reporting of the cognitive data. A pseudo-transition matrix, giving the probability that a triad is reported as one type when data are first taken, and a different type at a later date, is calculated. This compares reasonably with a genuine transition matrix evaluated for longitudinal cognitive data. It is believed that no data currently exist which can disprove this hypothesis, unlikely though it is. Much more accurate data are therefore necessary if any reliable theory of social structure is to be produced. [ABSTRACT FROM AUTHOR]

This paper describes the design and implementation of a "pre-structured multi-purpose data base" for information about the Canadian corporate structure. This system includes data on directorship, officership, executive board membership, and ownership ties among approximately 10,000 Canadian and other financial and industrial corporations and about 6,000 organizations (law firms, brokerage houses, public institutions, etc.) with which directors resident in Canada were affiliated. In addition, it contains data on the operating accounts, and standard industrial classification codes, for a large subset of these. Here we summarize its capabilities and analytic uses. [ABSTRACT FROM AUTHOR]

A developed theory of social networks would potentially provide predictive and explanatory models for social processes at the most general level. The paper contributes to such a theory by elaborating one basic proposition: that social connections attract each other as a regular function of network parameters such as `structural strength' (number of common links) and `distance' (length of minimal path of linkage). The proposition is tested on longitudinal data from three locality-based networks. [ABSTRACT FROM AUTHOR]

This paper examines whether clique-structure in cognitive data (i.e. recall of who one talks to) may be used as a proxy for clique-structure in behavioral data (i.e. who one actually talks to). The answer to this question is crucial to much of sociometric and social net-theoretic studies of social structure. We analysed the clique structures of the communication patterns of four naturally occurring groups of sizes 34 to 58, whose actual communications could easily be monitored, together with the groups' perceptions of their communications. The groups used were: radio hams, a college fraternity, a group of office workers, and an academic department. The analysis used clique-finding, block-modelling, and factor-analytic techniques, all employed in such a way as to maximize the accuracy of the cognitive data. After defining a way to compare clique structures between behavioral and cognitive data, we found that there was no useful relationship between the two, and furthermore there was no significant difference in performance between any of the structure-finding algorithms. We conclude that cognitive data may not be used for drawing any conclusions about behavioral social structure. [ABSTRACT FROM AUTHOR]

Analysis of an elementary level of social structure may be approached through a systematic description of who has access to whom. "Access" itself is a potential and cannot be directly measured, but differential actual acquaintanceship among sets of individuals can be presumed to reflect degrees of access. The paper presents a preliminary quantitative analysis of the systematic relationships shown by the patterns of acquaintanceship in several small social networks in the metropolitan New York area. [ABSTRACT FROM AUTHOR]

In this paper it is argued that, for the sake of analytical precision, we ought to understand structural-functionalism to be a social network theory, as opposed to the common practice of dissociating the two. The rise of 'network theory' against tile background of traditional structural-functionalism is reviewed, and the appreciation by some anthropologists that social structure is itself in fact an abstraction from social networks is noted. In a more original vein, it is shown that some network theories have themselves possessed a functional form. [ABSTRACT FROM AUTHOR]

Social networks have been closely identified with graph theoretical models, which constitute their most familiar mode of representation. There are a number of such models which may embody symmetric, directed, or valued relationships. But the study of networks with valued linkages, using the natural formalization provided by the valued graph or digraph, has been impeded by a traditional lack of analytical machinery for dealing with valued structures. In this paper, we demonstrate the development and elaboration of formalizations for the central network concepts of reachability, joining, and connectedness through graph theoretical models of increasing complexity, culminating in their expression within a general model for valued structures. This model for valued (symmetric or directed) graphs, or vigraphs, provides a unified representation and matrix methodology for dealing with qualitative and quantitative structures, incorporates many existing methods as special cases, and suggests new applications. Some of the most interesting of these follow the recognition, consistent with the model, that the "values" assigned to network linkages may be sorts of entities other than numbers. [ABSTRACT FROM AUTHOR]

Granovetter's 'strength of weak ties' theory offers a satisfying approach to the study of integration in networks of face-to-face interaction consisting of multiple subgroups. The present paper tests five hypotheses of this theory in the setting of a multidisciplinary social network of biological scientists. Considerable support for the theory is indicated: the local bridges and inter- group ties in the network are disproportionately weak ties. [ABSTRACT FROM AUTHOR]

Very little is known of the resilience of social networks in situations where individuals within a social network remain in situ, but the physical links which enable interaction between them are radically altered. This paper examines the long-term disruption of social networks following the collapse of the Tasman Bridge in Hobart, Tasmania. This accident divided the city in two for almost three years and radically altered normal patterns of mobility and accessibility. [ABSTRACT FROM AUTHOR]

This paper attempts to draw detailed parallels between the characterization and control of behavior in terms of the principles of psychology developed by B.F. Skinner, known as operant psychology or behavior analysis, and the characterization and control of behavior in the modern, factory work place. The authors argue that while behavior in the workplace now seems to conform to Skinnerian or operant principles, it did not in an earlier time, prior to the development of industrial capitalism.

In this paper the authors will explicitly take the cognitive content of a specialty within particle physics into account as they demonstrate how national differences in intellectual foci in the physics of weak interactions can be seen as a function of the overall position of a nation's scientists in the international communication system in weak interactions, the national availability of particle accelerator technology, and the interaction of these two with the process of international scientific competition. In particular, the authors will maintain that aggregate variations in problem selection among physicists from the U.S., Europe, Russia and Japan can be explained in part by 'national' variations along these two dimensions.

The article presents information related to research on the implementation of educational change. Research on the implementation of educational programs has a short, but intensive history of less than ten years. This research is increasingly sophisticated and cumulative in identifying with greater clarity the complexity and elusive nature of implementation. The purpose of this review is to characterize the current state of knowledge of implementation research. The theme of this paper is that the nature of the implementation process has been greatly misunderstood and underestimated and, indeed, is so complex that it is not as amenable to being managed as many policymakers and administrators would like. The process of implementation, however, is capable of being understood even if it cannot be managed effectively. To the extent that more people understand implementation, the chances for more effective planning and coping with educational change are increased. The subject of planning and coping with educational change is enormously large and cannot be treated adequately in this paper. Some of the main types of implications include, attempting fewer innovations, but doing them more carefully, not doing anything with particular innovations if there is insufficient commitment and resources to support implementation, use available research knowledge such as reviewed in this paper to design more sophisticated implementation plans.

This paper outlines and illustrates the application of loglinear models for characterizing the structural parameters of groups, as conceptualized by Blau (1974, 19 77). Models for nominal parameters are those in which an ingroup-outgroup distinction is embodied. Models for graduated parameters introduce distance effects. These models appear to be useful supplements to spatial techniques for identifying patterns of differential association, and they have implications for the calculation of proximity estimators in the use of those techniques. [ABSTRACT FROM AUTHOR]

The article presents response by the authors to the critical comments made by sociologists R.S. Burt and William M. Bittner on the works of the authors. First, Burt and Bittner questioned the scope of the authors' article. They argue that one cannot extend the scope of the conclusions from one network analysis to other systems. In authors' view, this misses the point entirely. In the series of papers written on informant accuracy the authors have never drawn conclusions about the structure of any group studied, let alone extended any conclusions about social structure to other groups or to the world at large. What authors have been studying is not groups, but the methods by which most researchers have gathered data about groups. It is about these methods that authors have drawn a global generalization from their seven data sets: the method by which data are traditionally obtained (some variant of "who do you interact with") does not yield any reliable information whatsoever about who people in the group actually interact with.

Let some individuals selected from a population form a subgroup. Let each individual name those individuals whom he considers to be the best members of his subgroup. Based on the number of times an individual was so named, we wish to find the probability that the individual is the best, second best, third best, etc., member of the population. This paper presents a method for the calculation of such probabilities. In so doing, it also offers a solution to the constant frame of reference problem in which individuals from different subgroups must be compared. [ABSTRACT FROM AUTHOR]

Network sampling is a potentially invaluable method of studying density of large networks, but its feasibility in practice is largely unknown. Two pre- tests of a network sampling instrument in a favourable setting (a network with moderate size, high density, and cooperative respondents) with a relatively representative population are reported in this paper. The results indicate that network sampling is indeed viable in such settings. Some suggestions for successful applications are offered. [ABSTRACT FROM AUTHOR]

The aim of this paper is relatively limited and modest: to classify and discuss the various models which have been and could be used to signify the relevance of the Western crime control experience for the Third World. While the implicitly relevant literature-for example, on the anthropology of law or on the nature of development is vast and complex, the explicit literature on crime in the Third World is sparse and poor. Criminologists have either ignored the Third World completely or treated it in a most theoretically primitive fashion, while the general literature on development and colonialism is remarkably silent about crime. Current systems of crime and deviance control in Western industrialized societies, originated in those three great historical transformations which took place from the end of the eighteenth to the beginning of the nineteenth centuries, first, the development of a centralized state apparatus for the control of crime and the care of dependency, second, the increasing differentiation of the deviant and dependent into separate types, each with its own attendant body of "scientific" knowledge and accredited experts; and, finally, the increased segregation of deviants and dependents into "asylums," mental hospitals, prisons, reformatories and other such closed, purpose-built institutions for treatment, punishment and custody.

This paper examines the roles women perform as terrorists and political criminals, using as much data as we could locate from a variety of countries and historical periods. But we acknowledge at the outset that our data describe only a small proportion of the known terrorists organizations. The tries to collect information from a variety of historical periods, nationalities and cultures, in the hope that this approach would allow us to throw light upon some current misconceptions about the female terrorist. Unfortunately, the available information is unsystematic, and largely anecdotal. Thus, it forms a weak foundation for sociological generalization. Because of the anecdotal nature of our information, we can draw only a roughly sketched collective profile of the typical female terrorist and discuss only briefly the roles that women have played and continue to play in terrorist groups. If the women's liberation movement has brought about an increase in the participation of women in radical and terrorist groups, then one would expect that prior to the women's liberation movement the role of women in radical political protests would be much less noticeable.

The article informs that it has become fashionable to lament the lack of influence of social science in important decisions. Whether the complaint is based upon fact or not, the number of social scientists who point out the underutilization of social science seems to grow with each issue of the leading journals. Beyond compendia of some years ago and a few expositions of general applications to "policy," there are comparatively few case studies tying concrete events to manipulation of social science findings. This paper is an attempt to use a specific case of social science information-a criminal court proceeding involving a public opinion poll-to show the special view some people take toward social science as "scientific evidence" and to show how the courts in particular might better use social science. This paper will show that different conceptions of what constitutes evidence or "fact" may be at the heart of the apparent underutilization of social science. Still, the social scientists' special environment does not coincide with the institutional environment of the policy maker. Social scientists start out questioning how they can increase the use of research during the decision making.

One of the recurrent problems in the study of social organization is that survey researchers are forced to study individuals, while they are often interested in hypotheses about organizations or systems of organizations. This paper offers some methods which allow survey researchers to address hypotheses about the relations generated among individuals by organizations, the organizations themselves, and the relations among organizations. Estimators are developed for the number and size distribution of organizations in communities, the density of relations among individuals generated by organizations, the number and density of inter organizational linkages, and the amount of membership overlap among organizations. This approach combines Granovetter's idea of network sampling with Breiger's notion of the duality of persons and groups to produce a quantitative approach to the study of voluntary organization. We provide an illustration of the methods we develop by testing two of Blau's structural hypotheses on data concerning voluntary organizations. The hypotheses that structural differentiation increases with system size and that this increase is at a decreasing rate are strongly supported. The paper closes with some suggestions for further elaborations of the hyper network approach. [ABSTRACT FROM AUTHOR]

Although the concept friend' is critical to both theoretical and empirical studies of social relations, it is a very ambiguous term. Most researchers seem to take its meaning for granted. This paper reports an inductive study designed to find out what aspects of real relations are correlated with applications of the label friend'. In a cross-sectional survey of 1050 adults living in northern California in 19 77, we obtained the names and descriptions of 19417 associates. Of these, 59% were labelled friends. Several regression analyses suggest that this label is likely to be applied: to an overwhelming majority of non-relatives in a largely unsystematic way; to associates lacking other, specialized role-relations; to people of the same age; to people known a long time; and to people with whom respondents had primarily sociable, rather than intimate or material, involvements. [ABSTRACT FROM AUTHOR]