  For any given graph $H$, one may define a natural corresponding functional
$\|.\|_H$ for real-valued functions by using homomorphism density. One may also
extend this to complex-valued functions, once $H$ is paired with a
$2$-edge-colouring $\alpha$ to assign conjugates. We say that $H$ is
real-norming (resp. complex-norming) if $\|.\|_H$ (resp. $\|.\|_{H,\alpha}$ for
some $\alpha$) is a norm on the vector space of real-valued (resp.
complex-valued) functions. These generalise the Gowers octahedral norms, a
widely used tool in extremal combinatorics to quantify quasirandomness. We
unify these two seemingly different notions of graph norms in real- and
complex-valued settings. Namely, we prove that $H$ is complex-norming if and
only if it is real-norming and simply call the property norming. Our proof does
not explicitly construct a suitable $2$-edge-colouring $\alpha$ but obtains its
existence and uniqueness, which may be of independent interest. As an
application, we give various example graphs that are not norming. In
particular, we show that hypercubes are not norming, which resolves the last
outstanding problem posed in Hatami's pioneering work on graph norms.
