  Protein-protein interaction networks associated with diseases have gained
prominence as an area of research. We investigate algebraic and topological
indices for protein-protein interaction networks of 11 human cancers derived
from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a
strong correlation between relative automorphism group sizes and topological
network complexities on the one hand and five year survival probabilities on
the other hand. Moreover, we identify several protein families (e.g. PIK, ITG,
AKT families) that are repeated motifs in many of the cancer pathways.
Interestingly, these sources of symmetry are often central rather than
peripheral. Our results can aide in identification of promising targets for
anti-cancer drugs. Beyond that, we provide a unifying framework to study
protein-protein interaction networks of families of related diseases (e.g.
neurodegenerative diseases, viral diseases, substance abuse disorders).
