Describe the matrices and formulae used to determine centralization or distribution of data
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Answer:
Step-by-step explanation:The idea of the centrality of individuals and organizations in their social networks was one of the earliest to be pursued by social network analysts. The immediate origins of this idea are to be found in the sociometric concept of the 'star' - that person who is the most 'popular' in his or her group or who stands at the centre of attention. The formal properties of centrality were initially investigated by Bavelas (1950), and, since his pioneering work, a number of competing concepts of centrality have been proposed. As a result of this proliferation of formal measures of centrality, there is considerable confusion in the area. What unites the majority of the approaches to centrality is a concern for the relative centrality of the various points in the graph the question of so-called 'point centrality'. But from this common concern they diverge sharply. In this chapter I will review a number of measures of point centrality, focusing on the important distinction between 'local' and 'global' point centrality. A point is locally central if it has a large number of connections with the other points in its immediate environment if, for example, it has a large 'neighbourhood' of direct contacts. A point is globally central, on the other hand, when it has a position of strategic significance in the overall structure of the network. Local centrality is concerned with the relative prominence of a focal point in its neighbourhood, while global centrality concerns prominence within the whole network.
Related to the measurement of point centrality is the idea of the overall 'centralization' of a graph, and these two ideas have sometimes been confused by the use of the same term to describe them both. Freeman's important and influential study (1979), for example, talks of both 'point centrality' and 'graph centrality'. Confusion is most likely to be avoided if the term ;centrality' is restricted to the idea of point centrality, while the term 'centralization' is used to refer to particular properties of the graph structue as a whole. Centralization, therefore, refers not to the relative prominence of points, but to the overall cohesion or integration of the graph. Graphs may, for example, be more or less centralized around particular points or sets of points. A number of different
86 Social network analysis
procedures have been suggested for the measurement of centralization, contributing further to the confusion which besets this area. Implicit in the idea of centralization is that of the structural 'centre' of the graph, the point or set of points around which a centralized graph is organized. There have been relatively few attempts to define the idea of the structural centre of a graph, and it will be necessary to give some consideration to this.
Centrality: Local and Global
The concept of point centrality, I have argued, originated in the sociometric concept of the 'star'. A central point was one which was 'at the centre' of a number of connections, a point with a great many direct contacts with other points. The simplest and most straightforward way to measure point centrality, therefore, is by the degrees of the various points in the graph. Tle degree, it will be recalled, is simply the number of other points to which a point is adjacent. A point is central, then, if it has a high degree; the corresponding agent is central in the sense of being 'well-connected' or 'in the thick of things'. A degree-based measure of point centrality, therefore, corresponds to the intuitive notion of how well connected a point is within its local environment. Because this is calculated simply in terms of the number of points to which a particular point is adjacent, ignoring any indirect connections it may have, the degree can be regarded as a measure of local centrality. The most systematic elaboration of this concept is to be found in Nieminen (1974). Degree-based measures of local centrality can also be computed for points in directed graphs, though in these situations each point will have two measures of its local centrality, one corresponding to its indegree and the other to its outdegree. In directed graphs, then, it makes sense to distinguish between the 'in-centrality' and the 'out-centrality' of the various points.