Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. A number of methods have been proposed to measure aspects of the structure of such networks, but a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex.
Topology of loopy network architectures
Monday, November 7, 2011 - 12:00pm to 1:00pm
Joseph Henry Room, Jadwin Hall