Almulhim, F, Thwaites, PA orcid.org/0000-0001-9700-2245 and Taylor, CC orcid.org/0000-0003-0181-1094 (2019) A New Approach to Measuring Distances in Dense Graphs. In: Machine Learning, Optimization and Data Science. Lecture Notes in Computer Science . Springer, Cham , pp. 204-216. ISBN 978-3-030-13708-3
Abstract
The problem of computing distances and shortest paths between vertices in graphs is one of the fundamental issues in graph theory. It is of great importance in many different applications, for example, transportation, and social network analysis. However, efficient shortest distance algorithms are still desired in many disciplines. Basically, the majority of dense graphs have ties between the shortest distances. Therefore, we consider a different approach and introduce a new measure to solve all-pairs shortest paths for undirected and unweighted graphs. This measures the shortest distance between any two vertices by considering the length and the number of all possible paths between them. The main aim of this new approach is to break the ties between equal shortest paths SP, which can be obtained by the Breadth-first search algorithm (BFS), and distinguish meaningfully between these equal distances. Moreover, using the new measure in clustering produces higher quality results compared with SP. In our study, we apply two different clustering techniques: hierarchical clustering and K-means clustering, with four different graph models, and for a various number of clusters. We compare the results using a modularity function to check the quality of our clustering results.
Metadata
Item Type: | Book Section |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2019. This is a post-peer-review, pre-copyedit version of a chapter published in Lecture Notes in Computer Science volume 11331. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-13709-0_17. |
Keywords: | Network; Adjacency matrix; K-means clustering; Hierarchical clustering; Modularity function |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 May 2019 09:35 |
Last Modified: | 14 Feb 2020 01:39 |
Status: | Published |
Publisher: | Springer, Cham |
Series Name: | Lecture Notes in Computer Science |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:145957 |