Abstract: We present the results of an experimental and numerical study of the distributions of the imaginary and real parts, P(v) and P(u), of Wigner's reaction K matrix for irregular, tetrahedral graphs in the presence of an absorption. In the experiment we used microwave graphs (networks), which were built of coaxial cables and attenuators connected by T-joints. Distributions of the imaginary and real parts of K matrix were obtained from the measurements and numerical calculations of thescattering matrix $S$ of the networks, respectively. We show that the experimental and numerical results are in good agreement with the theoretical predictions.