  We present the first experimental evidence for the multifractality of a
transport property at a topological phase transition. In particular, we show
that conductance fluctuations display multifractality at the
integer-quantum-Hall $\nu=1 \longleftrightarrow \nu=2$ plateau-to-plateau
transition in a high-mobility mesoscopic graphene device. We establish that to
observe this multifractality, it is crucial to work with very high-mobility
devices with a well-defined critical point. This multifractality gets rapidly
suppressed as the chemical potential moves away from these critical points. Our
combination of multifractal analysis with state-of-the-art transport
measurements at a topological phase transition provides a novel method for
probing such phase transitions in mesoscopic devices.
