Graph Curvature for Differentiating Cancer Networks

Area of Science:

• Graph theory
• Systems biology
• Genomics

Background:

• Cellular interactions are modeled as weighted graphs, where network function depends on topology and geometry.
• Understanding network properties is crucial for analyzing biological systems, particularly in disease states like cancer.

Purpose of the Study:

• To apply graph curvature to gene co-expression networks from cancer genomic studies.
• To determine if graph curvature can differentiate between cancer and normal biological samples.
• To identify novel gene-gene interactions affected by cancer.

Main Methods:

• Utilized geometric notions of curvature on weighted graphs.
• Analyzed gene co-expression networks from large-scale cancer genomic data.
• Quantitatively related graph curvature to network entropy.
• Developed an exact mathematical solution for calculating pair-wise curvature changes.

Main Results:

• Cancer gene networks exhibit significantly higher curvature than normal networks.
• Graph curvature reliably distinguishes between cancer and normal samples.
• Identified novel, disrupted pair-wise gene interactions in cancer samples.
• Established a quantitative link between graph curvature and network entropy.

Conclusions:

• Graph curvature is a robust indicator for distinguishing cancer from normal biological networks.
• This approach reveals previously unidentified disrupted gene-gene interactions in cancer.
• The developed mathematical framework enables precise analysis of complex biological networks, paving the way for new analytical methods.