2MRS and 6dF galaxies. The 6dF sample of 126754 sources is limited in magnitudes by $m_{\rm K} \leq$ 12.65, $m_{\rm H} \leq$ 12.95, $m_{\rm J} \leq$ 13.75, $m_{\rm r_{\rm F}} \leq$ 15.60 and $m_{\rm b_{\rm J}} \leq$ 16.75, and has a median redshift of 0.053 [@art:6df3]. In the case of 2MRS, the sample contains 44599 galaxies and is limited in magnitude by $m_{\rm K_{\rm s}} \leq 11.75$. The survey only probes out to redshifts of $z \approx$ 0.05, but it covers a larger area of the sky than the other two surveys [@art:2mrs]. Because the 2MRS galaxies are used in both filament catalogues, there will be some overlap between the filament spines derived from them.\

Noise estimation {#sec:noise}
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The signal-to-noise ratio of a filament depends on both the signal itself and on the noise originating from the instrument and the survey characteristics. We assume every filament has the same signal, so that the S/N only varies depending on the filament size on the sky and the telescope sensitivity.\
For the integration of the signal in real data, the filament would be split up into resolution elements, whose angular size corresponds to the filament diameter of $0.5~h^{-1}$Mpc. However, since the 