Graph comparison via the nonbacktracking spectrum
Abstract
The comparison of graphs is a vitally important, yet difficult task which arises across a number of diverse research areas including biological and social networks. There have been a number of approaches to define graph distance, however, often these are not metrics (rendering standard datamining techniques infeasible) or are computationally infeasible for large graphs. In this work we define a new pseudometric based on the spectrum of the nonbacktracking graph operator and show that it cannot only be used to compare graphs generated through different mechanisms but can reliably compare graphs of varying size. We observe that the family of WattsStrogatz graphs lie on a manifold in the nonbacktracking spectral embedding and show how this metric can be used in a standard classification problem of empirical graphs.
 Publication:

Physical Review E
 Pub Date:
 May 2019
 DOI:
 10.1103/PhysRevE.99.052309
 arXiv:
 arXiv:1812.05457
 Bibcode:
 2019PhRvE..99e2309M
 Keywords:

 Computer Science  Social and Information Networks;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 11 pages, 5 figures, 2 tables