  We calculate measures of hierarchy in gene and tissue networks of breast
cancer patients. We find that the likelihood of metastasis in the future is
correlated with increased values of network hierarchy for expression networks
of cancer-associated genes, due to correlated expression of cancer-specific
pathways. Conversely, future metastasis and quick relapse times are negatively
correlated with values of network hierarchy in the expression network of all
genes, due to dedifferentiation of gene pathways and circuits. These results
suggest that hierarchy of gene expression may be useful as an additional
biomarker for breast cancer prognosis.
