This research presents a new method to estimate the local road vehicle miles traveled (VMT) with the concept of betweenness centrality. Betweenness centrality is a measure of a node's or link's centrality on a network that has been applied popularly in social science and we relate it to traffic volumes. We demonstrate that VMT on local roads exhibits a scale-free property: it follows two piecewise (double) power law distributions. In other words, the total local VMT can be obtained by properly connecting the two distributions at a breakpoint, each having a slope of the power law distribution. We show that the breakpoint can be predicted by using certain network topological measures, which indicates that the breakpoint may be an inherent property for a particular network. We also show that the highest betweenness centrality point can be estimated using network measures. Furthermore, we prove that the estimated VMT is not sensitive to the power of the power law distributions. This research highlights a potentially new direction of effort for local road VMT estimation. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151794