The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 33
The following text was automatically extracted from the image on this page using optical character recognition software:
represent the number of geodesic paths from s to t and gst(i) the number of geodesic paths from s
to t that contain i. Now the probability, bst(i), that point i lies on a randomly selected path from s
to point t is shown in Equation (15).
To consider the overall betweenness centrality of point i which includes all geodesic paths in
the network, CB(i), the sum of all partial betweenness values is calculated as shown in Equa-
tion (16). Since CB(i) is simply a count, the relative potential based on the size of the network is
not taken into consideration. A relative betweenness value, CA (i) as shown in (18), can be derived
by expressing this value as a ratio of CB (i) to the maximum betweenness value possible in a net-
work of size n. The maximum betweenness value, maxCB(i) as shown in Equation (17), occurs
when a node i falls on every geodesic path connecting all nodes not including i.
(15) bst(i) (1st (gst(i)) =gst(i)g
(16) CB(i) - 3 bst (i)
s= 1 t=s+1
(17) maxCB(i) [n(n 1)] n-1] n22 3n + 2
(18) Cn(i) =2CB()
n2 - 3n + 2
Information Centrality. Information centrality is based on the same concept as betweenness
centrality, but also considers the degrees of the nodes along each network path. When betweenness
centrality is calculated, it is assumed that two geodesic paths are equally likely to be "chosen" and
therefore the probability of each geodesic path is identical. It may be presumed that vertices along
the path which have a high degree are more likely to be on a "chosen" geodesic path. An even
Here’s what’s next.
This dissertation can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Dissertation.
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/m1/43/: accessed May 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .