We compute the galaxy-galaxy correlation function of low-luminosity SDSS-DR7 galaxies $(-20 < M_{rm r} - 5log_{10}(h) < -18)$ inside cosmic voids identified in a volume limited sample of galaxies at $z=0.085$. To identify voids, we use bright galaxies with $M_{rm r} - 5log_{10}(h) < -20.0$. We find that structure in voids as traced by faint galaxies is mildly non-linear as compared with the general population of galaxies with similar luminosities. This implies a redshift-space correlation function with a similar shape than the real-space correlation albeit a normalization factor. The redshift space distortions of void galaxies allow to calculate pairwise velocity distributions which are consistent with an exponential model with a pairwise velocity dispersion of $w sim 50-70$ km/s, significantly lower than the global value of $w sim 500$ km/s. We also find that the internal structure of voids as traced by faint galaxies is independent of void environment, namely the correlation functions of galaxies residing in void-in-void or void-in-shell regions are identical within uncertainties. We have tested all our results with the semi-analytic catalogue MDPL2-textsc{Sag} finding a suitable agreement with the observations in all topics studied.
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