A Pascal program to generate objective indices of group or organizational structures

Abstract

As an adjunct to developing a theory of structural roles, a mathematical model of group or organizational struc­ ture was developed (Oeser & Harary, 1962, 1964; Oeser & O'Brien, 1967). This paper briefly describes the model, the generated quantitative structural indices, and a Pas­ cal program to compute the indices. The Mathematical Model Organizational or group structure is described by three elements: persons (h), positions (p), and tasks (t), and the five relations between these elements. The relations are the informal relations between persons (H-H), the assign­ ment relations between persons and positions (H-P), the power relations between positions (P-P) , the allocation relations between positions and task (P-T), and the prece­ dence relations between tasks (T-T). The structure may be represented schematically as in Figure 1. Each element is represented by a dot, and the relations are represented by directed arrows between the elements. Figure 1 represents a three-person (h., h2 , h.), three-position (p., P2, P3), three-task (t., t 2, t3) group. Each person is as­ signed to one position, and each position is allocated to one task element. Position P2 has legitimate power over positions PI and P3 and this is represented by directed lines from P2 to PI and P3' The arrows between the task ele­ ments indicate that the group is performing a coordina­ tive or assembly-line-type task. Person hi is assigned to position PI and completes the first part of the task, t., which is then passed to person h, at position P2, and so on. The informal relations or communication network be­ tween persons is similarly represented by directed lines between the person elements (h., h2 , h.). The set of five relations may also be represented in matrix form. The matrices for the set of relations described in Figure 1 are presented in Table 1. A matrix entry of 1 indicates the presence of a relation beween two elements, and an entry of 0 indicates the absence of a re­ lation. Matrix entries can also be a decimal value greater than 0 to indicate both the presence and strength of a re­ lation. The organizational or group structure is represented in matrix form because matrix algebra is used to gener­ ate quantitative structural indices.