  Based on the optimal quantum violation of suitable Bell's inequality, the
device-independent self-testing of state and observables has been reported. It
is well-studied that locally commuting or compatible observables cannot be used
to reveal quantum nonlocality. Therefore, the self-testing of commuting local
observables cannot be possible through the Bell test. In this work, we
demonstrate the self-testing of a set of mutually commuting local observables.
Such certification has not hitherto been reported. We show that the optimal
quantum violations of suitably formulated bilocality and n-locality
inequalities in networks uniquely fix the observables of one party to be
mutually commuting. In particular, we first demonstrate that in a
two-input-arbitrary-party star network, two commuting local observables can be
self-tested. Further, by considering an arbitrary-input three-party bilocal
network scenario, we demonstrate the self-testing of an unbounded number of
mutually commuting local observables.
