Chronic low back pain (LBP) is one of the leading causes of disability worldwide. While LBP research has largely focused on the spine, many studies have demonstrated a restructuring of human brain architecture accompanying LBP and other chronic pain states. Brain imaging presents a promising source for discovering noninvasive biomarkers that can improve diagnostic and prognostication outcomes for chronic LBP. This study evaluated graph theory measures derived from brain resting-state functional connectivity (rsFC) as prospective noninvasive biomarkers of LBP. We also proposed and tested a hybrid feature selection method (Enet-subset) that combines Elastic Net and an optimal subset selection method. We collected resting-state functional MRI scans from 24 LBP patients and 27 age-matched healthy controls (HC). We then derived graph-theoretical features and trained a support vector machine (SVM) to classify patient group. The degree centrality (DC), clustering coefficient (CC), and betweenness centrality (BC) were found to be significant predictors of patient group. We achieved an average classification accuracy of 83.1% (p < 0.004) and AUC of 0.937 (p < 0.002), respectively. Similarly, we achieved a sensitivity and specificity of 87.0 and 79.7%. The classification results from this study suggest that graph matrices derived from rsFC can be used as biomarkers of LBP. In addition, our findings suggest that the proposed feature selection method, Enet-subset, might act as a better technique to remove redundant variables and improve the performance of the machine learning classifier.