Spectral Goodness of Fit for Network Models

23 Pages Posted: 26 Jul 2014

See all articles by Jesse Shore

Jesse Shore

Boston University - Questrom School of Business

Benjamin Lubin

Boston University - Questrom School of Business

Date Written: July 24, 2014

Abstract

We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure how well a network model explains the structure of an observed network. SGOF provides an absolute measure of fit, analogous to the standard R-squared in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.

Keywords: social networks, complex systems, network models, goodness of fit, spectral graph theory

JEL Classification: C00

Suggested Citation

Shore, Jesse and Lubin, Benjamin, Spectral Goodness of Fit for Network Models (July 24, 2014). Boston U. School of Management Research Paper No. 2471270, Available at SSRN: https://ssrn.com/abstract=2471270 or http://dx.doi.org/10.2139/ssrn.2471270

Jesse Shore (Contact Author)

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

HOME PAGE: http://jesseshore.com

Benjamin Lubin

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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