  Aims. This work provides an analysis of how the galaxy number density of the
input data affects the filaments detected with the Bisous filament finder and
gives estimates of the reliability of the method itself to assess the
robustness of the results.
  Methods. We applied the Bisous filament finder to MultiDark-Galaxies data,
using various magnitude cuts from the catalogue to study the effects of
different galaxy number densities on the results and different parameters of
the model. We compared the structures by the fraction of galaxies in filaments
and the volume filled by filaments, and we analysed the similarities between
the results from different cuts based on the overlap between detected
filamentary structures. The filament finder was also applied to the exact same
data 200 times with the same parameters to study the stochasticity of the
results and the correlation between different runs was calculated.
  Results. Multiple samples show that galaxies in filaments have preferentially
higher luminosity. We found that when a galaxy is in a filament there is a 97%
chance that the same galaxy would be in a filament with even more complete
input data and about 85% of filaments are persistent when detecting the
filamentary network with higher-density input data. Lower galaxy number density
inputs mean the Bisous model finds fewer filaments, but the filaments found are
persistent even if we use more complete input data for the detection. We
calculated the correlation coefficient between 200 Bisous runs on the exact
same input, which is 0.98.
  Conclusions. This study confirms that increased number density of galaxies is
important to obtain a more complete picture of the cosmic web. To overcome the
limitation of the spectroscopic surveys, we will develop the Bisous model
further to apply this tool to combined spectroscopic and narrow-band
photometric redshift surveys, such as the J-PAS.
