  The carbon isotope $^{13}$C, in contrast to $^{12}$C, possesses a nuclear
magnetic moment and can induce electron spin dephasing in graphene. This effect
is usually neglected due to the low abundance of $^{13}$C in natural carbon
allotropes ($\sim$1 %). Chemical vapor deposition (CVD) allows for artificial
synthesis of graphene solely from a $^{13}$C precursor, potentially amplifying
the influence of the nuclear magnetic moments. In this work we study the effect
of hyperfine interactions in pure $^{13}$C-graphene on its spin transport
properties. Using Hanle precession measurements we determine the spin
relaxation time and observe a weak increase of $\tau_{s}$ with doping and a
weak change of $\tau_{s}$ with temperature, as in natural graphene. For
comparison we study spin transport in pure $^{12}$C-graphene, also synthesized
by CVD, and observe similar spin relaxation properties. As the signatures of
hyperfine effects can be better resolved in oblique spin-valve and Hanle
configurations, we use finite-element modeling to emulate oblique signals in
the presence of a hyperfine magnetic field for typical graphene properties.
Unlike in the case of GaAs, hyperfine interactions with $^{13}$C nuclei
influence electron spin transport only very weakly, even for a fully polarized
nuclear system. Also, in the measurements of the oblique spin-valve and Hanle
effects no hyperfine features could be resolved. This work experimentally
confirms the weak character of hyperfine interactions and the negligible role
of $^{13}$C atoms in the spin dephasing processes in graphene.
