Degree Year
2017
Document Type
Thesis - Open Access
Degree Name
Bachelor of Arts
Department
Mathematics
Advisor(s)
Elizabeth L. Wilmer
Keywords
Graph theory, Random graph, Network, Small world network, Watts-Strogatz, Shortest path, Graph diameter
Abstract
We study a novel model of random graph which exhibits the structural characteristics of the Watts- Strogatz small-world network. The small-world network is characterized by a high level of local clustering while also having a relatively small graph diameter. The same behavior that makes the Watts-Strogatz model behave like this also makes it difficult to analyze. Our model addresses this issue, closely mimicking the same structure experimentally while following a constructive process that makes it easier to analyze mathematically. We present a bound on the average shortest path length in our new model, which we approach by looking at the two key geometric components.
Repository Citation
Allen, Andrea J., "Average Shortest Path Length in a Novel Small-World Network" (2017). Honors Papers. 181.
https://digitalcommons.oberlin.edu/honors/181
