The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 31
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TABLE 2.4. Relative degree centrality measures for vertices in Figure 2.14
quickly influence other nodes in the network. Unlike degree centrality, closeness centrality takes
into account indirect as well as direct connections. It is reasonable to expect that the duration of
an outbreak will be influenced if individuals with a high degree of closeness become infected, as
these individuals are tightly connected to the rest of the population. In Figure 2.15, although sev-
eral other nodes have a higher degree centrality, Node 5 is at most two hops from any other node
in the network, making it the most important node based upon closeness centrality (see Table 2.5).
Closeness centrality of a node, Co(i), is calculated as shown in Equation (13). In this equation,
d(i, j) refers to the geodesic distance from node i to node j. Some formulas for closeness do not
take the reciprocal of the summation of the distances, however when a node is a greater distance
away, the centrality should decrease. Therefore, the geodesic distances should be weighted in-
versely. The maximum closeness value is obtained when a node is directly connected to every
other node in the network. In a network of size n, the maximum closeness is 1 Thus, a relative
closeness centrality, C(i), is calculated by multiplying by n - 1 as shown in Equation (14).
(14) Co(i) n - 1 (n - 1)Cc(i)
j= i ,j )
v C (v) v CD5(v)
1 0.2 7 0.4
2 0.2 8 0.1
3 0.3 9 0.3
4 0.8 10 0.5
5 0.1 11 0.3
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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/m1/41/: accessed May 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .