  Cancer heterogeneity arises from complex molecular interactions. Elucidating
systems-level properties of gene interaction networks distinguishing cancer
from normal cells is critical for understanding disease mechanisms and
developing targeted therapies. Previous works focused only on identifying
differences in network structures. In this study, we used graph frequency
analysis of cancer genetic signals defined on a co-expression network to
describe the spectral properties of underlying cancer systems. We demonstrated
that cancer cells exhibit distinctive signatures in the graph frequency content
of their gene expression signals. Applying graph frequency filtering, graph
Fourier transforms, and its inverse to gene expression from different cancer
stages resulted in significant improvements in average F-statistics of the
genes compared to using their unfiltered expression levels. We propose graph
spectral properties of cancer genetic signals defined on gene co-expression
networks as cancer hallmarks with potential application for differential
co-expression analysis.
