Topological data analysis (TDA) has established itself as a useful tool for capturing multiscale structures in complex networks, such as connected components, cycles, and cavities. Although Vietoris-Rips (VR) filtering is widely used in network analysis, it tends to be computationally expensive, especially for large networks. This work explores vertex function-based (VFB) filtering based on network measures, applying persistent homology to identify relevant topological structures in cancer-associated protein networks, and compares its effectiveness with the VR approach. The results show that VFB reproduces the second-order structures (Betti-2) identified by VR, recovering previously reported essential genes. In addition, VFB detected new driver genes, confirmed in databases such as IntOGen and NCG, and allowed analysis of third-order structures (Betti-3) that was not feasible with VR. Thus, VFB represents a scalable alternative to VR, preserving biological interpretability and complementing classical network metrics.
@article{arxiv.2605.11450,
title = {Scalable vertex guided filtrations identify structurally relevant genes in cancer networks},
author = {Edmara Viana and Rodrigo Henrique Ramos and Flávia Raquel Gonçalves Carneiro and Cynthia de Oliveira Lage Ferreira},
journal= {arXiv preprint arXiv:2605.11450},
year = {2026}
}