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Recent estimations of the Hubble parameter $H_0$ based on gravitational waves(GW) observations can be used to shed some light on the discrepancy between thevalue of the Hubble parameter $H_0^P$ obtained from large scale observationssuch as the Planck mission, and the small scale value $H_0^R$, obtained fromlow redshift supernovae (SNe).  In order to investigate the origin of this discrepancy we perform a combinedanalysis of the luminosity distance of SNe and GW sources, using differentmethods, finding that the impact of the GW data is very limited, due to thesmall number of data points, and their large errors. We analyze separately datafrom the Pantheon and the Union 2.1 catalogues, finding that a model with$H_0^P$ and a small local void can fit the data as well as a homogeneous modelwith $H_0^R$, resolving the apparent $H_0$ tension. We find that there is asignificant difference between the size and depth of the inhomogeneity obtainedusing the two datasets, which could be due to the different sky coverage of thetwo catalogues. For Pantheon we obtain evidence of a local inhomogeneity with adensity contrast $\delta_v=-0.155 \pm 0.026$, extending up to a redshift of$z_v = 0.056 \pm 0.0002$, while for Union 2.1 we obtain $\delta_v=-0.461 \pm0.032$ and $z_v= 0.081\pm 0.008$. We also perform some analysis using redshiftshell averaged data, and obtain approximately the same results, hinting to thefact that the effects of the monopole component of the local inhomogeneity arethe dominant ones

Combining gravitational and electromagnetic waves observations to investigate local structure and the Hubble tension