Nonisomorphic two‐dimensional algebraically defined graphs over R <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23161:jgt23161-math-0001" wiley:location="equation/jgt23161-math-0001.png"><mrow><

Abstract For , let be a two‐dimensional algebraically defined graph, that is, a bipartite graph where each partite set is a copy of and two vertices and are adjacent if and only if . It is known that has girth 6 and can be extended to the point‐line incidence graph of the classical real projective plane. However, it was unknown whether there exists such that has girth 6 and is nonisomorphic to . This paper answers this question affirmatively and thus provides a construction of a nonclassical real projective plane. This paper also studies the diameter and girth of for families of bivariate functions .