Experimental investigation of properties of hexagon networks with and without time reversal symmetry

We present the results of experimental study of the distribution P(R) of the reflection coefficient R and the distributions of Wigner's reaction K matrix for irregular hexagon fully connected microwave networks simulating quantum graphs with time reversal symmetry (TRS)in the presence of absorption. The distributions of the reflection coefficient R and the real and imaginary parts of K matrix were obtained from the measurements of the scattering matrix S of the microwave networks. Furthermore, we show that the microwave networks with microwave circulators can be used to study systems with broken TRS. Properties of such networks are investigated using the cross-correlation function c(12)(nu) and the integrated nearest-neighbor spacing distribution I(s).