  One of the most challenging problems in biomedicine and genomics is the
identification of disease biomarkers. In this study, proteomics data from seven
major cancers were used to construct two weighted protein-protein interaction
(PPI) networks i.e., one for the normal and another for the cancer conditions.
We developed rigorous, yet mathematically simple, methodology based on the
degeneracy at -1 eigenvalues to identify structural symmetry or motif
structures in network. Utilising eigenvectors corresponding to degenerate
eigenvalues in the weighted adjacency matrix, we identified structural symmetry
in underlying weighted PPI networks constructed using seven cancer data.
Functional assessment of proteins forming these structural symmetry exhibited
the property of cancer hallmarks. Survival analysis refined further this
protein list proposing BMI, MAPK11, DDIT4, CDKN2A, and FYN as putative
multi-cancer biomarkers. The combined framework of networks and spectral graph
theory developed here can be applied to identify symmetrical patterns in other
disease networks to predict proteins as potential disease biomarkers.
