  We present the results of experimental and theoretical study of irregular,
tetrahedral microwave networks consisting of coaxial cables (annular
waveguides) connected by T-joints. The spectra of the networks were measured in
the frequency range 0.0001-16 GHz in order to obtain their statistical
properties such as the integrated nearest neighbor spacing distribution and the
spectral rigidity. The comparison of our experimental and theoretical results
shows that microwave networks can simulate quantum graphs with time reversal
symmetry. In particular, we use the spectra of the microwave networks to study
the periodic orbits of the simulated quantum graphs. We also present
experimental study of directional microwave networks consisting of coaxial
cables and Faraday isolators for which the time reversal symmetry is broken. In
this case our experimental results indicate that spectral statistics of
directional microwave networks deviate from predictions of Gaussian orthogonal
ensembles (GOE) in random matrix theory approaching, especially for small
eigenfrequency spacing s, results for Gaussian unitary ensembles (GUE).
Experimental results are supported by the theoretical analysis of directional
graphs.
