Expected normalized correlation functions for the masked version (Sect. 3.2) of the noise-free (and also without any contamination) fields that are shown in Fig. 2. The blue line points up the auto-correlation function for the modeled filament y-map (left panel in Fig. 2). Red dashed line shows the cross-correlation function between filament y-map and galaxy density map (right panel in Fig. 2). The characteristic statistical feature of these filamentary structures in terms of correlation degree is obviously seen as a bump in large scales roughly between 30 and 40 degrees, which is shown with a gray band. This scale corresponds to the average separation between primary elongation occurrences of the filamentary structures, as the bump in correlation function indicates that there should be a specific repetitive interval within the analyzed topology.