  We describe a category of undirected graphs which comes equipped with a
faithful functor into the category of (colored) modular operads. The associated
singular functor from modular operads to presheaves is fully faithful, and its
essential image can be classified by a Segal condition. This theorem can be
used to recover a related statement, due to Andr\'e Joyal and Joachim Kock,
concerning a larger category of undirected graphs whose functor to modular
operads is not just faithful but also full.
