  We suggest that the gauge-invariant hedgehoglike structures in the Wilson
loops are physically interesting degrees of freedom in the Yang--Mills theory.
The trajectories of these ``hedgehog loops'' are closed curves corresponding to
center-valued (untraced) Wilson loops and are characterized by the center
charge and winding number. We show numerically in the SU(2) Yang--Mills theory
that the density of hedgehog structures in the thermal Wilson--Polyakov line is
very sensitive to the finite-temperature phase transition. The (additively
normalized) hedgehog line density behaves like an order parameter: the density
is almost independent of the temperature in the confinement phase and changes
substantially as the system enters the deconfinement phase. In particular, our
results suggest that the (static) hedgehog lines may be relevant degrees of
freedom around the deconfinement transition and thus affect evolution of the
quark-gluon plasma in high-energy heavy-ion collisions.
