Experimental and theoretical study of irregular microwave graphs (networks) consisting of coaxial cables connected by the joints are presented. The spectra of the microwave networksare measured for bidirectional and directional microwave networks consisting of coaxial cables and Faraday isolators for which the time reversal symmetry is broken. In this way the statistical properties of the graphs such as the integrated nearest neighbor spacing distribution and the spectral rigidity are obtained.We show that microwave irregular microwave networks with absorption can be used to experimental studies of the distributions of Wigner's reaction K matrix. The distributions of the imaginary and real parts of K matrix, P(v) and P(u), respectively, are obtained from the measurements and numerical calculations of the scattering matrix S of the networks. We demonstrate that the experimental and numerical results are in good agreement with the theoretical predictions. Furthermore, we present the results of studies of parameter dependent velocity correlation functions in the graphs.