We experimentally investigate the diagonal elements of the Wigner’s reaction \({\hat{ K}}\) matrix in the undirected open microwave network \({\Gamma } \) with internal absorption composed of two coupled directed unidirectional networks \({\Gamma }_{+} \) and \({\Gamma }_{-} \) . The two-port scattering matrix \({\hat{S}}\) of the network \({\Gamma }\) is measured and the distributions of the imaginary P(v) and real P(u) parts of the diagonal elements of the Wigner’s reaction matrix are evaluated. Additionally, the distributions P(R) and P(r) of the reflection coefficient R and the amplitude r of the diagonal elements of the scattering matrix \({\hat{S}}\) of the network are respectively assessed. We show that though the network \({\Gamma } \) is characterized by time reversal symmetry its characteristics are closely described by the Gaussian unitary ensemble predictions in random matrix theory.