  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.
