Observation of Gravitional waves by LIGO from binary black hole merger I read the paper "Observation of Gravitational Waves from a Binary Black Hole Merger"
https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102

I tried to understand all the graphs and data observed in the paper.
I am curious how these data and graphs conclude that the gravitational waves observed were because of binary black holes merger? Also what calculations and equations led to the same?
Also how will the calculations and equations look if neutron stars were there instead of black hole in the same merger?

(graphs and data can be seen in the observation section in the paper)
Neutron stars are less massive but larger than black holes. The frequency of the gravitational waves is due to the orbital period of the objects as they spiral together. A neutron star merger would have a different orbital speed, so the frequency would be different and lower. It would rise at a different rate. The signal from neutron stars is also much weaker, so couldn't be detected from the same range.

Prior to the detection of the signal, numerical simulations of merging black holes of various sizes were done, so the theoretical shape of the waveform expected from the merger of black holes (and neutron stars) was known. It was possible from this theoretical work to estimate the mass of the two black holes taking part in the merger by matching the observed signal to a theoretical one. You can see the theoretical signal for black holes with 36 and 29 in the diagrams labelled as "numerical relativity"