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Most proposed DHTs engage certain topology maintenance mechanisms specific to the static graphs on which they are based. The designs of these mechanisms are complicated and repeated with graph-relevant concerns. In this paper, we propose the “distributed line graphs” (DLG), a universal technique for designing DHTs based on arbitrary regular graphs. Using DLG, the main features of the initial graphs are preserved, and thus people can design a new DHT by simply choosing the graph with desirable features and applying DLG to it. We demonstrate the power of DLG by illustrating four DLG-enabled DHTs based on different graphs, namely, Kautz, de Bruijn, butterfly, and hypertree graphs. The effectiveness of our proposals is demonstrated through analysis, simulation, and implementation.