The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L p Wasserstein distances between probability measures, we define the corresponding spectral distances d p 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 d 1 , is one. We further study the behavior of d 1 when the size of graphs tends to infinity by interlacing inequalities aiming at exploring large real networks. A monotonic relation between d 1 and the evolutionary distance of biological networks is observed in simulations.
Gu et al. REF defined a spectral distance by assigning a probability measure to the nodes via the spectrum representation of each graph, and by using Wasserstein distances between probability measures.
Spectral distances on graphs
Discrete Applied Mathematics 190/191 (2015), 56-74
Mathematics Physics Computer Science