The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 27
This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided to UNT Digital Library by the UNT Libraries.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
FIGURE 2.11. Ordered graph example
Although regular graphs represent contacts with neighbors, other interactions that are known
to exist in real social networks are not accurately represented. Such interactions are those that
frequently occur in daily life when meetings occur between two people who are not normally in
the same social circle. This includes contacts that take place while in a grocery store, on vaca-
tion, riding in public transportation, standing in line at an event, or a number of other similar
situations. Even in very large social networks, the small-world effect theorizes that any two peo-
ple are connected by a relatively short chain of intermediate contacts [60]. A small-world graph
is a model based on the small-world effect. It is a structure that falls between a random graph
and an ordered lattice, exhibiting the clustering behavior of an ordered graph while maintaining
the small-world property observed in random graphs. First introduced in the mid-1950's, small-
world graphs gained scientific popularity after a publication by Watts and Strogatz in 1998 [70].
Since that time, many researchers have explored the properties and applications of small-world
graphs [22, 43, 47, 52, 60].
A small-world graph can be easily constructed from an ordered lattice by rerouting some of the
edges [80]. Each edge may be rerouted to another vertex based on some probability, p. A value
of p = 0 results in a completely ordered graph and a value of p = 1 creates a random graph. A27
Upcoming Pages
Here’s what’s next.
Search Inside
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/m1/37/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .