The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 54
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disease spread where repeated contacts increase the likelihood that a disease will transfer from one
individual to another. Outlined below are centrality measures designed specifically for the purpose
of identifying individuals in a social network who are more prone to facilitate disease spread.
4.2.1. Contact Centrality
Contact Centrality measures the number of contacts an individual makes within a unit of time,
including those contacts which are unique and those which are repeated. Represented in a graph,
an edge with a weight of 1 between two nodes is initially created upon the first contact between
the two nodes. Each additional contact between the same two nodes increases the edge weight by
one. The contact centrality for node i, CN(i), is calculated as a sum of the edge weights between i
and all neighbors of i. This is easily calculated through the use of an adjacency matrix, Aij. Each
entry in Aij represents the weight of the edge between i andj. This calculation (see Equation 20)
is identical to that of degree centrality presented previously with the exception that the adjacency
matrix is weighted rather than binary.
DEFINITION 4.1. Contact centrality is defined as the average number of contacts an individual
makes within a specified unit of time.
(20) CN (z)= 3
j 1,~ CN(i)
(21) Cj(i) nl- nn
i=1 j=i+1 i=1 j=i+1
Contact centrality is illustrated in Figure 4.1. In this graph, Node 4 has a contact centrality of
16 which is the highest value in this network. The edge weight of 7 between nodes 1 and 4 implies
that 7 contacts are made between these two individuals that are capable of disease transfer if one
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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/m1/64/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .