random graphs in a gin are good for graph isomorphism

For maximum expressivity, we can use a GIN with white, anonymous inputs. That is,

• Each $x_i=1$
• Each ${\hat{x}}_i=1$

However, designing a white inputs requires computing eigendecomposition which is expensive.

Instead, we usually relax this condition to random inputs, which almost surely satisfy ${\hat{x}}_i=1$.

^statement