Maryam Pouryahya, Rena Elkin, Romeil Sandhu, Sarah Tannenbaum, Tryphon Georgiou, and Allen Tannenbaum
nternational Symposium on Mathematical Theory of Networks and Systems
Publication year: 2016

In this note, we describe a methodology based on the discretization of Bakry-Emery Ricci curvature for weighted graphs with an emphasis on studying cancer networks from The Cancer Genome Atlas (TCGA) . In particular, we utilize the Gamma-2 calculus of Bakry-Emery which suggest a discrete notion analogous to curvature in the general framework of a Markov semigroup.  The condition is based on the Bochner inequality with dimension condition CD(K,N).   This said, the empirical study focuses on illuminating differences between normal and cancer tissue derived from a variety of publicly available cancer samples in TGCA.  The goal here is to continually build on an existing framework that shows curvature as a potential “cancer hallmark”.