The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 59
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calculate spread centrality, Cs(i), is the sum of the geodesic distances from i to j, d(i, j), for all
points j - i as given in Equation 26. The formula for spread centrality is the same as that for close-
ness centrality except that geodesic distances are calculated as discussed above for transmission
DEFINITION 4.3. Spread centrality is defined as the weighted social distance between an individ-
ual and every other individual in the social network.
Normalization for spread centrality must consider edge weights in addition to size of the graph.
Normalization for closeness centrality is achieved by multiplying the raw value by n-1. This stan-
dardizes across any network size so that the maximum closeness of any node is obtained when that
node is connected to every other node and the normalized value is unity. In a weighted graph, a
maximum normalized value of unity for spread centrality is obtained when the unweighted nor-
malization is divided by the maximum weight evenly distributed over all other nodes as shown in
(26) Cs (i) -=1 d(ij)
(n - 1 2 1
(n-1) CS(Z) (n-1)2 C
(2s7) Cs(i) = ()
i=1 j=i+1 i=1 j=i+1
4.3. Simulating an Outbreak on an Established Contact Graph
The third and final stage of the experiments presented herein is the simulation of outbreaks
across an established contact network once central nodes have been vaccinated. Outbreaks are
based on the susceptible-infectious-removed (SIR) model discussed in Chapter 2. Disease param-
eters are defined in Table 4.2. The total number of contacts for the entire population is calculated
as the size of the population, N, times the average number of contacts per person, per day, CR.
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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/m1/69/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .