The detection of the gravitational wave events GW150914, GW151226, LVT 151012 and GW170104 by the Advanced LIGO antennas has opened a new possibility for the study of fundamental physics of gravitational interaction. We suggest a new method for determining the polarization state of a gravitational wave, which is independent of the nature of a GW source. For this, we calculate the allowed sky positions of GW sources along apparent circles. This is done for each polarization state by considering the sensitivity pattern of each antenna and relative amplitudes of detected signals. The positions of circles are calculated with respect to the line joining both LIGO antennas using the observed arrival time delay of the signal between them. The apparent circles (AC) on the sky for allowed positions of the GW sources for the GW150914, GW151226 and LVT151012 events are parallel to the plane of the disc-like large scale structure known as the Local Super-Cluster (LSC) of galaxies which extends up to radius $sim 100$ Mpc and having thickness $sim 30$ Mpc. For the GW170104 event, the AC is perpendicular to the LSC plane but the predicted position of the source may also belong to the LSC plane, which is consistent with detection of possible optical counterpart ATLAS17aeu. The next aLIGO-aVirgo observing runs are proposed to test the possibility of clustering the GW sources along the LSC plane.
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