  We investigate properties of the transmission amplitude of quantum graphs and
microwave networks composed of regular polygons such as triangles and squares.
We show that for the graphs composed of regular polygons with the edges of the
length $l$ the transmission amplitude displays a band of transmission
suppression with some narrow peaks of full transmission. The peaks are
distributed symmetrically with respect to the symmetry axis $kl=\pi$, where $k$
is the wave vector. For microwave networks the transmission peak amplitudes are
reduced and their symmetry is broken due to the influence of internal
absorption. We demonstrate that for the graphs composed of the same polygons
but separated by the edges of length $l' < l$ the transmission spectrum is
generally not symmetric according to the axis $kl'=\pi$. We also show that
graphs composed of regular polygons of different size with the edges being
irrational numbers are not fully chaotic and their level spacing distribution
and the spectral rigidity are well described by the Berry-Robnik distributions.
Moreover, the transmission spectrum of such a graph displays peaks which are
very close to $1$. Furthermore, the microwave networks are investigated in the
time-domain using short Gaussian pulses. In this case the delay-time
distributions, though very sensitive to the internal structure of the networks,
show the sequences of transmitted peaks with the amplitudes much smaller than
the input one. The analyzed properties of the graphs and networks suggest that
they can be effectively used to manipulate quantum and wave transport.
