# Testing properties of graphs and functions

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DOI: 10.1007/s11856-010-0060-7

- Cite this article as:
- Lovász, L. & Szegedy, B. Isr. J. Math. (2010) 178: 113. doi:10.1007/s11856-010-0060-7

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## Abstract

We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the function values as edge probabilities. We give a characterization of properties testable this way, and extend a number of results about “large graphs” to this setting.

These results can be applied to the original graph-theoretic property testing. In particular, we give a new combinatorial characterization of the testable graph properties. Furthermore, we define a class of graph properties (flexible properties) which contains all the hereditary properties, and generalize various results of Alon, Shapira, Fischer, Newman and Stav from hereditary to flexible properties.