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This article introduces a network model that pictures occupants of robust positions as recipients of diversified support from durably located others and portrays occupants of fragile positions as dependents on tenuously situated others. The model extends Herfindahl's index of concentration by bringing in the recursiveness of Bonacich's method. Using Newcomb's study of a college fraternity, we find empirical support for the contention that fragility reduces future growth in status. Applications of the model to input-output networks among industries in the U.S. economy and to hiring networks among academic departments are also presented. Implications for future research are discussed.

Networks of several distinct types of social tie are aggregated by a dual model that partitions a population while simultaneously identifying patterns of relations. Concepts and algorithms are demonstrated in five case studies involving up to 100 persons and up to eight types of tie, over as many as 15 time periods. In each case the model identifies a concrete social structure. Role and position concepts are then identified and interpreted in terms of these new models of concrete social structure. Part II, to be published in the May issue of this Journal (Boorman and White 1976), will show how the operational meaning of role structures in small populations can be generated from the sociometric blockmodels of Part I.

Role structures in small populations are given operational meaning as algebras generated from the sociometric blockmodels of Part I by Boolean multiplication (matrix multiplication employing binary arithmetic). Many different sociometric structures can yield the same algebraic multiplication table, which captures a different level of social structure. Elements of the algebras are interpreted concretely as compound roles, and interlock among these roles is studied through investigation of their algebraic properties (equations and inclusions). Similarities and differences among algebras from six case studies are explored by means of homomorphisms as well as by multidimensional scaling on a derivative numerical distance measure. Results for particular populations, including reliability and stability tests, are summarized through simple target tables reporting aggregations of more complicated role structures.

Price and authority have traditionally been regarded as alternative social mechanisms for allocating resources. However, actual transactions-whether inter- or intrafirm-can be evaluated in terms of the extent to which they combine both of these mechanisms. An especially revealing example of this is the exchange of goods between two profit centers in the multi-profit center firm. Three of the most common arrangements, or transfer pricing polices, for effecting these transactions are examined here. Exchange autonomy transfers depend primarily on price, with no or minimal use of authority. Mandated full cost transfers involve a substantial exercise of authority relative to the use of price. Mandated market based transfers use both authority and price in important ways. For all three policies, the transaction costs of these internal transactions may exceed these costs on external transactions.

A new model for inheritance in intergenerational mobility is developed and related to mover-stayer models of intragenerational mobility. Application is made to data for the United States, Britain, and Denmark. Predictions are required to match observed proportions of men remaining in their origin strata and also the observed distribution of men among destination strata.

Simon's linear model for some of Homans's propositions about small groups is imbedded in a more general system of coupled linear differential equations in group averages as variables. It is successfully translated into differential equations about flows of proportions of men among cells in a cross-classification, equations adapted from Coleman's Introduction to Mathematical Sociology. Simon's unmeasurable averages are operationalized as the marginals in the 2 X 2 table and can be found directly from two coupled equations in the marginals, if the rate parameters satisfy certain constraints. An additional independent equation reflects a correlation of attributes across individuals not considered by Simon. Several ways to estimate parameters and test the model are discussed.

Three types of chronic conflict concerning research and development found in a medium-sized metallurgical company involve sixteen members of upper management. Selznick's model for the growth of autonomy in a bureaucracy is used in describing the general pattern of the conflicts. Differences in orientation to outside opinion and to uncertainty among the departments were decisive for the development of different departmental "ideologies" and strategies. Application of a procedure for inferring the structure of interpersonal relations from sociometric choices yields results supporting the interview-based analysis of conflicts. Recurrent revisions of formal structure and reallocations of responsibility for programs seemed to be distinctive concomitants of chronic conflict.