  We analyze the critical ultraviolet behaviour of the four-graviton amplitude
in N=8 supergravity to all order in perturbation. We use the
Bern-Carrasco-Johansson diagrammatic expansion for N=8 supergravity multiloop
amplitudes, where numerator factors are squares of the Lorentz factor of N=4
super-Yang-Mills amplitudes, and the analysis of the critical ultraviolet
behaviour of the multiloop four-gluon amplitudes in the single- and
double-trace sectors. We argue this implies that the superficial ultraviolet
behaviour of the four-graviton N=8 amplitudes from four-loop order is
determined by the factorization the k^8 R^4 operator. This leads to a
seven-loop logarithmic divergence in the four-graviton amplitude in four
dimensions.
