One of the challenges of brain network analysis is to directly compare network organization between subjects, irrespective of the number or strength of connections. In this study, we used minimum spanning tree (MST; a unique, acyclic subnetwork with a fixed number of connections) analysis to characterize the human brain network to create an empirical reference network. Such a reference network could be used as a null model of connections that form the backbone structure of the human brain. We analyzed the MST in three diffusion-weighted imaging datasets of healthy adults. The MST of the group mean connectivity matrix was used as the empirical null-model. The MST of individual subjects matched this reference MST for a mean 58%-88% of connections, depending on the analysis pipeline. Hub nodes in the MST matched with previously reported locations of hub regions, including the so-called rich club nodes (a subset of high-degree, highly interconnected nodes). Although most brain network studies have focused primarily on cortical connections, cortical-subcortical connections were consistently present in the MST across subjects. Brain network efficiency was higher when these connections were included in the analysis, suggesting that these tracts may be utilized as the major neural communication routes. Finally, we confirmed that MST characteristics index the effects of brain aging. We conclude that the MST provides an elegant and straightforward approach to analyze structural brain networks, and to test network topological features of individual subjects in comparison to empirical null models.