  The resistance $R$ vs perpendicular external magnetic field $H$ was measured
for superconducting Nb thin--film microbridges with and without microholes
[antidots (ADs)]. Well below the transition temperature, integral $R(H)$
measurements of the resistive transition to the normal state on the plain
bridge show two distinct regions, which can be identified as bulk and edge
superconductivity, respectively. The latter case appears when bulk
superconductivity becomes suppressed at the upper critical field $H_{c2}$ and
below the critical field of edge superconductivity $H_{c3}\approx 1.7\,
H_{c2}$. The presence of additional edges in the AD bridge leads to a different
shape of the $R(H)$ curves. We used low-temperature scanning laser microscopy
(LTSLM) to visualize the current distribution in the plain and AD bridge upon
sweeping $H$. While the plain bridge shows a dominant LTSLM signal at its edges
for $H > H_{c2}$ the AD bridge also gives a signal from the inner parts of the
bridge due to the additional edge states around the ADs. LTSLM reveals an
asymmetry in the current distribution between left and right edges, which
confirms theoretical predictions. Furthermore, the experimental results are in
good agreement with our numerical simulations (based on the time-dependent
Ginzburg--Landau model) yielding the spatial distribution of the order
parameter and current density for different bias currents and $H$ values.
