The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 55
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individual is infectious and the other is susceptible. Likewise, there are 9 possible opportunities for
transfer between nodes 4 and 8. A measure of non-weighted degree centrality in this same network
would identify Node 3 as the most central, even though Node 3 makes fewer overall contacts than
FIGURE 4.1. Contact centrality illustrated by Node 4
Degree centrality is normalized by dividing each centrality measure by the number of possible
edges, which is n - 1 in a graph of size n. Because the weight of edges in a weighted graph is
potentially unlimited, contact centrality is normalized by dividing by the total of all edge weights.
Like standard normalization techniques, this will produce a centrality value between 0 and 1, in-
clusive. A normalized contact centrality of 0 indicates that the node is disconnected, as illustrated
by Node 3 in Figure 4.2. A normalized contact centrality of 1 indicates that the graph is structured
as a star or wheel, as illustrated by Node 4 in Figure 4.3. The formula for normalized contact
centrality of Node i, Cp(i), is given in Equation 21. This is simply the contact centrality of Node
i divided by the sum of half of the undirected weighted adjacency matrix.
FIGURE 4.2. Disconnected node with a contact centrality of 0 illustrated by Node 8
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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/m1/65/: accessed May 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .