The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 29
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FIGURE 2.13. Hypergraph example
2.4.3. Centrality Measures
Point centrality, also referred to as node centrality, is used to determine which nodes are the
most important in a graph . Importance, of course, is relative to the purpose of the graph. For
the purpose of this research, importance refers to the ability to transfer a disease. Of four centrality
measures outlined by Wasserman and Faust in "Social Network Analysis" , Degree, Close-
ness, and Betweenness were implemented for this research. Although there are other measures of
centrality, these three were selected to represent the structure of a graph. The initial software for
this research was validated using the centrality indices for Padgett's Florentine families as shown
in . A description and example of each of these centrality measures is outlined below.
Degree Centrality. Degree centrality is the most straightforward to compute because it is
simply a count of the number of edges incident to a node. An individual with more connections to
other individuals may be deemed more important. Degree centrality can be calculated for a point in
a graph of size n as shown in Equation (11). CD (i), the degree centrality of node i, is the sum of all
adjacent nodes as indicated by Aj, the adjacency matrix. In Figure 2.14, it is easily observed that
Node 4 is of degree 8 and could be regarded as the most important node in the network. However,
a degree of size 8 in a much larger graph might be comparatively small. It is common to normalize
centrality measures to produce a value that is independent of the graph size. The largest possible
degree of a node in a graph of size n is n - 1. Therefore, Equation (12) can be used to calculate
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Johnson, Tina V. The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment, dissertation, December 2010; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc33173/m1/39/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .