Abstract Fast radio bursts (FRBs) represent one of the most intriguing phenomena in modern astrophysics. However, their classification into repeaters and nonrepeaters is challenging. Here, we present the application of the graph theory minimum spanning tree (MST) methodology as an unsupervised classifier of repeater and nonrepeater FRBs. By constructing MSTs based on various combinations of variables, we identify those that lead to MSTs that exhibit a localized high density of repeaters at each side of the node with the largest betweenness centrality. Comparing the separation power of this methodology against known machine learning methods, and with the random expectation results, we assess the efficiency of the MST-based approach to unravel the physical implications behind the graph pattern. We finally propose a list of potential repeater candidates derived from the analysis using the MST.