Persistent homology method to detect block structures in weighted networks

The paper’s CRVR definition plus its own visual cue (a red vertical line at x=1) implies that with ζ=1 the filtration is constant for t≥1; yet multiple core claims rely on births after t>1 and H2 deaths at t=10, which contradict the CRVR construction as stated. For example, the text asserts (for assortative and related variants) that “some H1 barcodes [are] born after t=1” and “lots of H2 barcodes die at t=10, the maximum distance,” alongside figure captions marking x=1 as a key threshold and weights drawn from [1,10] within and [0,1] between groups. These statements are internally inconsistent unless ζ≪1; but the paper nowhere specifies ζ and repeatedly treats 1 as a decisive boundary, making its t-scale incoherent. The model solution diagnoses this ‘cropping barrier’ precisely and corrects each sub-claim (i)–(iv), and it further refutes the ER/WSBM ‘classification’ claims with sound asymptotic reasoning. In short, the paper’s conclusions depend on a mis-specified/unstated ζ and conflate weight and distance scales, whereas the model provides a consistent, quantified analysis.