A LinearTime Algorithm and Analysis of Graph Relative Hausdorff Distance
Abstract
Graph similarity metrics serve farranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative Hausdorff (RH) distance is a promising, recently proposed measure for quantifying degree distribution similarity. In spite of recent interest in RH distance, little is known about its properties. Here, we conduct an algorithmic and analytic study of RH distance. In particular, we provide the first lineartime algorithm for computing RH distance, analyze examples of RH distance between families of graphs, and prove several analytic results concerning the range, density, and extremal behavior of RH distance values.
 Authors:

 BATTELLE (PACIFIC NW LAB)
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1569008
 Report Number(s):
 PNNLSA141641
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Journal Article
 Journal Name:
 SIAM Journal on Mathematics of Data Science
 Additional Journal Information:
 Journal Volume: 1; Journal Issue: 4
 Country of Publication:
 United States
 Language:
 English
 Subject:
 Relative Hausdorff distance, degree distribution, network science
Citation Formats
Aksoy, Sinan G., Nowak, Kathleen E., and Young, Stephen J. A LinearTime Algorithm and Analysis of Graph Relative Hausdorff Distance. United States: N. p., 2019.
Web. doi:10.1137/19M1248224.
Aksoy, Sinan G., Nowak, Kathleen E., & Young, Stephen J. A LinearTime Algorithm and Analysis of Graph Relative Hausdorff Distance. United States. doi:10.1137/19M1248224.
Aksoy, Sinan G., Nowak, Kathleen E., and Young, Stephen J. Tue .
"A LinearTime Algorithm and Analysis of Graph Relative Hausdorff Distance". United States. doi:10.1137/19M1248224.
@article{osti_1569008,
title = {A LinearTime Algorithm and Analysis of Graph Relative Hausdorff Distance},
author = {Aksoy, Sinan G. and Nowak, Kathleen E. and Young, Stephen J.},
abstractNote = {Graph similarity metrics serve farranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative Hausdorff (RH) distance is a promising, recently proposed measure for quantifying degree distribution similarity. In spite of recent interest in RH distance, little is known about its properties. Here, we conduct an algorithmic and analytic study of RH distance. In particular, we provide the first lineartime algorithm for computing RH distance, analyze examples of RH distance between families of graphs, and prove several analytic results concerning the range, density, and extremal behavior of RH distance values.},
doi = {10.1137/19M1248224},
journal = {SIAM Journal on Mathematics of Data Science},
number = 4,
volume = 1,
place = {United States},
year = {2019},
month = {10}
}