Romeil Sandhu, Sarah Tannenbaum, Tryphon Georgiou, and Allen Tannenbaum
IEEE Conference on Decision and Control
Publication year: 2016

In this note, we extend the notion of Ollivier-Ricci curvature on weighted graphs with all positive weights to the case in which the weights may also be negative. This is done by employing the Hahn-Jordan decomposition of signed measures, allowing us to extend the Earth Mover’s Distance to an extended class of measures. The resulting curvature will be utilized to study the robustness properties of general networks. In particular, this will be applied to certain cancer transcription networks in order to elucidate fragility with respect to those genes responsible for maintaining cellular homeostasis related to growth and proliferation.