  Can one hear the shape of a graph? This is a modification of the famous
question of Mark Kac "Can one hear the shape of a drum?" which can be asked in
the case of scattering systems such as quantum graphs and microwave networks.
It addresses an important mathematical problem whether scattering properties of
such systems are uniquely connected to their shapes? Recent experimental
results based on a characteristics of graphs such as the cumulative phase of
the determinant of the scattering matrices indicate a negative answer to this
question (O. Hul, M. Lawniczak, S. Bauch, A. Sawicki, M. Kus, L. Sirko, Phys.
Rev. Lett 109, 040402 (2012).). In this paper we consider important local
characteristics of graphs such as structures of resonances and poles of the
determinant of the scattering matrices. Using these characteristics we study
experimentally and theoretically properties of graphs and directly confirm that
the pair of graphs considered in the cited paper is isoscattering. The
experimental results are compared to the theoretical ones for a broad frequency
range from 0.01 to 3 GHz. In the numerical calculations of the resonances of
the graphs absorption present in the experimental networks is taken into
account.
