Spectral distances on graphs

Gu, Jiao; Hua, Bobo; Liu, Shiping

Abstract

By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using Lp Wasserstein distances between probability measures, we define the corresponding spectral distances dp on the set of all graphs. This approach can even be extended to measuring the distances between infinite graphs. We prove that the diameter of the set of graphs, as a pseudo-metric space equipped with d1, is one. We further study the behavior of d1 when the size of graphs tends to infinity by interlacing inequalities aiming at exploring large real networks. A monotonic relation between d1 and the evolutionary distance of biological networks is observed in simulations.

Citation

Gu, J., Hua, B., & Liu, S. (2015). Spectral distances on graphs. Discrete Applied Mathematics, 190-191, 56-74. https://doi.org/10.1016/j.dam.2015.04.011

• Journal Article Type: Article
• Acceptance Date: Apr 16, 2015
• Publication Date: Aug 20, 2015
• Deposit Date: Mar 16, 2015
• Publicly Available Date: Jun 4, 2015
• Journal: Discrete Applied Mathematics
• Print ISSN: 0166-218X
• Electronic ISSN: 1872-6771
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 190-191
• Pages: 56-74
• DOI: https://doi.org/10.1016/j.dam.2015.04.011
• Keywords: Wasserstein distance, Spectral measure, Random rooted graph, Asymptotic behavior, Biological networks.
• Public URL: https://durham-repository.worktribe.com/output/1444162