von Nasrullah Memon
Statistik und Sichtungsnachweis dieser Seite findet sich am Artikelende
| [1.] Nm/Fragment 102 02 - Diskussion Zuletzt bearbeitet: 2012-04-29 14:03:01 WiseWoman | Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Scott 1987, Verschleierung |
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| Untersuchte Arbeit: Seite: 102, Zeilen: 2-28 |
Quelle: Scott_1987 Seite(n): 83-85, Zeilen: p. 83: 33- |
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| A degree based measure of node centrality can be extended beyond direct connections to those at various path distances. In this case, the relevant neighbourhood is widened to include the more distant connections of the nodes. A node may, then, be assessed for its local centrality in terms of both direct (distance 1) and distance 2 connections—or, indeed, whatever cut-off path distance is chosen. The principal problem with extending this measure of node centrality beyond distance 2 connections is that, in graphs with even a very modest density, the majority of the nodes tend to be linked through indirect connections at relatively short path distances.
Thus a comparison of local centrality scores at a distance 4 is unlikely to be informative if most of the nodes are connected to most other nodes at this distance. The degree, therefore, is a measure of local centrality, and a comparison of the degrees of various nodes in a graph can show how well connected the nodes are with their local environments. This measure of local centrality has one major limitation. That is comparisons of centrality scores can only meaningfully be made among members of the same graph or between graphs that are the same size. The degree of a node depends on, among other things, the size of the graph, and so measure of local centrality cannot be compared when graphs differ significantly in size. Local centrality is, however, only one conceptualization of node centrality, and Freeman (1979, 1980) has proposed a measure of global centrality based around what he terms the closeness of the nodes. |
A degree-based measure of point centrality can be extended beyond direct connections to those at various path distances. In this case, the relevant 'neighbourhood' is widened to include the more distant connections of the points. A point may, then, he assessed for its local centrality in terms of both direct (distance 1) and distance 2 connections or, indeed, whatever cut-off path distance is chosen. The principal problem with extending this measure of point centrality beyond distance 2 connections is that, in graphs with even a very modest density, the majority of the points tend to be linked through indirect connections at relatively short path distances. Thus, comparisons of local centrality wares at distance 4, for example, are [EN 87] unlikely to be informative if most of the points are connected to
[p. 84] most other points at this distance. [...] The degree, therefore, is a measure of local centrality, and a comparison of the degrees of the various points in a graph can show how well connected the points are with their local environments. This measure of local centrality has, however, one major limitation. This is that comparisons of centrality mores can only [EN 88] meaningfully be made among the members of the same graph [p. 85] or between graphs which are the same size. The degree of a point depends on, among other things, the size of the graph, and so measures of local centrality cannot be compared when graphs differ significantly in size. [...] Local centrality is, however, only one conceptualization of point centrality, and Freeman (1979, 1990) has proposed a measure of global centrality based around what he terms the 'closeness' of the points. [EN 87] [Bibliography is not available online] [EN 88] |
Scott is mentioned in the thesis for the first time on page 220. |
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