Scalable vertex guided filtrations identify structurally relevant genes in cancer networks

TL;DR

This paper introduces a scalable vertex function-based filtering method for topological data analysis in cancer networks, effectively identifying relevant genes and structures while reducing computational costs.

Contribution

The authors propose a vertex function-based filtering approach that efficiently captures topological features in large networks, outperforming traditional Vietoris-Rips filtering.

Findings

VFB reproduces second-order structures identified by VR.

VFB detects new driver genes confirmed in databases.

VFB enables analysis of third-order structures not feasible with VR.

Abstract

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.