Chapter 9: Analyzing Positions
9.1 Centrality Centrality, in general, is a property of points in a graph. Related to social capital, centrality can be used to measure the potential for access and control over information and resources. There are two conceptualizations of centrality of a point related to access: local and global. The measure of centrality related to control is often considered intermediate. A point is locally central if it has a large number of connections with the other points if it has a large neighborhood of direct contacts. A point is globally central if it has a position of strategic significance in the overall structure of the network – if it can reach other points on short paths. Local centrality is concerned with the relative activity of a focal point (called ego) in its neighborhood (of alters), while global centrality concerns reach within the whole network. 9.1.1 Degree The simplest and most straightforward measure of local centrality is called the degree of a point. The degree is simply the number of points to which a point is adjacent. A point is locally central if it has a high degree. For an undirected graph, the degree of a point is just the number of lines that are attached to the point. Working from the adjacency matrix, you can obtain this by summing across the row for the point. For directed graphs, we can distinguish between the number of lines with arrows coming in to the point (the InDegree, also the column sum of the adjacency...
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