Using Graph Theory to Compute Sets of Cycles in Vascular Networks

We use graph theory in conjunction with automated vessel data extraction software to identify and quantify looping structures in biological resource distribution networks. As a practical biomedical application, characterizations of looping structures may serve to non-invasively distinguish a pathological resource distribution network from a healthy one. A network with loops is structurally different from a network without loops and may result in a refined scaling exponent for metabolic rate. A refined scaling exponent would also have implications for aging, lifespan, and evolutionary development. Here we focus on developing mathematical tools to find looping structures in biological vascular networks. Looping structures in biological resource distribution networks can be extracted by using graph theory to quantify the cycle basis of the graph of the network. Algebraic ring sums are then used to quantify the total number of loops in the graph