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We consider the infinite family of Feynman graphs known as the "bananagraphs" and compute explicitly the classes of the corresponding graphhypersurfaces in the Grothendieck ring of varieties as well as theirChern-Schwartz-MacPherson classes, using the classical Cremona transformationand the dual graph, and a blowup formula for characteristic classes. We outlinethe interesting similarities between these operations and we give formulae forcones obtained by simple operations on graphs. We formulate a positivityconjecture for characteristic classes of graph hypersurfaces and discussbriefly the effect of passing to noncommutative spacetime.

Feynman motives of banana graphs