Chapter 8: Analyzing Structure
This chapter presents measures of the social structure of a network. The structure, as we have seen, is a key determinant of the amounts and types of social capital that members of the group or organization can tap into. Further, measures of structure will help to locate where social capital resides. 8.1 Global measures Let us add some new terminology. A complete graph is one in which all of the points are adjacent to one another: each point is connected directly to every other point. The density of a graph is the actual number of ties which are present, in comparison to the total number of ties which would be present if the graph were complete. In other words, density measures the percentage of pairs of persons who are tied by the social relation defining the graph. Note that density differs from the number of points that are included in any lines (or relations), which in comparison to the total number of points is referred to as the inclusiveness of the graph. Density is a measure of overall tie activity, rather than node participation. For an undirected graph, to get the number of ties we count the actual number of lines which are present in the sociograph. We could also get this by summing the upper triangular entries (above the diagonal) in the adjacency matrix. We then compare this count to the total number of lines which would be present if the graph were complete. For any undirected graph with...
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