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By S. D. Berkowitz

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Extra resources for An Introduction to Structural Analysis. The Network Approach to Social Research

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8. 0. 4, respectively. 20 Young and Willmott stress the importance of sheer geographic distance in altering the intensity of ties between members of the nuclear families living in "Greenleigh" and kin left behind in Bethnal Green. Thus, husbands who continued, on balance, to work in Bethnal Green, maintained slightly more contact with kinsmen than wives who, for the most part, did not. 2 1 From a structural point of view, this and related research undertaken by Young and Willmott 22 —though methodologically restricted by its failure to examine second-order and thirr 1 -order contacts—strongly suggests important analytic dimensions which were not present, to any significant extent, in Bott's work.

2 = "Liking" = Kinship 34 AN I N T R O D U C T I O N TO S T R U C T U R A L ANALYSIS In most cases, it is therefore simply a matter of convention whether or not we use arrowheads in depicting implicitly reciprocal relations. Assuming all things constant, both forms of the graph will yield the same matrix. " If we wanted to combine the friendship and kinship matrices shown above into one matrix indicating what Mitchell refers to as multiplexity, that is, the existence of multiple ties between nodes, we could simply sum these binary matrices together using the rules for matrix addition: Definition 1: Matrix A matrix, A, is a rectangular array of real numbers A = [a ,J,, that Γ fl n a vi · • fli/Π «22 · • 02/i [ßml dnvl · • Ö mn\ «21 such A = where i and ; refer to the row and column positions of an element within a matrix, and m and n are specified as the number of rows and number of columns, respectively.

As we noted earlier, however, both of these types of ties would normally be represented by identical entries in their respective matrices. To wit: Phase I Matrix Phase II Matrix g β α ß 0 1 1 0 0 1 {l_ 0 Thus, in order to analyze the process of merger, we must find some mathematically recognizable way of distinguishing between the reciprocal, but independent, emanations represented in the Phase I Matrix and the implicitly reciprocal relations shown in the Phase II Matrix. Structural analysts have devised two general ways of doing this.

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