  The overall aim of this paper is to define a structure of graph operads, thus
generalizing the celebrated pre-Lie operad on rooted trees. More precisely, we
define two operads on multigraphs, and exhibit a non trivial link between them
and the pre-Lie and Kontsevich- Willwacher operads. We study one of these
operads in more detail. While its structure is too involved to exhibit a
description by generators and relations, we show that it has interesting
finitely generated sub-operads, with links with the commutative and the
magmatic commutative operads. In particular, one of them is Koszul and this
allows us to compute its Koszul dual. Finally, we introduce a new framework on
species and operads and a general way to define operads on multigraphs.
