Exploring Real World Networks Via Parameter Vectors, Euclidean Distance and Graphs
| dc.contributor.author | Asare, Judith | |
| dc.contributor.copyright-release | Not Applicable | |
| dc.contributor.degree | Master of Science | |
| dc.contributor.department | Department of Mathematics & Statistics - Math Division | |
| dc.contributor.ethics-approval | Not Applicable | |
| dc.contributor.external-examiner | n/a | |
| dc.contributor.manuscripts | Not Applicable | |
| dc.contributor.thesis-reader | Dr. Jeannette Janssen | |
| dc.contributor.thesis-reader | Dr. Dorette Pronk | |
| dc.contributor.thesis-supervisor | Dr. Jason Brown | |
| dc.date.accessioned | 2025-08-14T14:38:10Z | |
| dc.date.available | 2025-08-14T14:38:10Z | |
| dc.date.defence | 2025-08-11 | |
| dc.date.issued | 2025-08-13 | |
| dc.description | Can the structure of a mouse’s brain bear any meaningful similarity to a social network like Facebook? While these systems differ in nature and function, both can be viewed through the lens of Graph Theory. This leads us to ask not only whether such similarities exist, but also how they can be measured and understood. Graphs have long served as a language for representing the structure of some real world systems, from communication infrastructure and transportation grids to biological systems and online social platforms . The strength of this framework lies in its ability to reduce highly complex systems to a form that is analyzable using well established mathematical tools. Comparing and contrasting graphs is not straightforward. We want our analyses to focus on the overall structure. Further, we want to be able to consider and compare graphs of vastly different sizes. An approach we consider here is collect data about each graph in the form of values of various graph parameters, perhaps normalized in some way so that none dominates the rest. In this process, we convert graphs into vectors, and we attempt to analyze graphs by the data points associated with them. With this connection, we talk about the distance between graphs using the Euclidean distance between their associated data points | |
| dc.description.abstract | This thesis explores a framework for analyzing collections of graphs by first associating each graph with a vector of graph-theoretic parameters. These parameters such as maximum and minimum degrees, connectivity and clustering coefficient serve as numerical summaries that enable quantitative comparisons between graphs. Once graphs are represented in this vector space, we apply two methods based on Euclidean distance to study relationships among them. The first method constructs a distance graph, in which each node corresponds to a graph in the dataset, and an edge is drawn between two nodes if the Euclidean distance between their associated vectors is below a specified threshold. This approach captures the notion of ”closeness” among graphs in terms of their structural features. The second method uses the Ball Mapper algorithm, a relatively new tool from Topological Data Analysis. Here, clusters of structurally similar graphs are formed by covering the dataset with overlapping balls in the parameter space. Each ball becomes a vertex in the resulting Ball Mapper graph, and edges connect balls that share at least one data point. This provides a compressed, topological summary of the entire graph collection. We applied these methods to three families of real world graphs obtained from the Network Repository: Animal Social Networks, Cheminformatics Networks, and Dynamic Networks. In total, 30 graphs were analyzed, 10 graphs from each category. While individual families often yielded disconnected graphs due to the small sample size, combining all three families resulted in richer structures, revealing meaningful clusters and connectivity patterns. Our findings highlight both the promise and challenges of using the Ball Mapper algorithm to study structural similarities in real world networks. | |
| dc.identifier.uri | https://hdl.handle.net/10222/85323 | |
| dc.language.iso | en | |
| dc.subject | Distance Graph | |
| dc.subject | BallMapper Graphs | |
| dc.title | Exploring Real World Networks Via Parameter Vectors, Euclidean Distance and Graphs |