Graph theory is the mathematical study of patterns and their properties without reference to any metrical information. The method proposed ('fishbone' method) allows the obtaining of 20 pieces of interrelated graphical information on the characteristics of each fingerprint, which are sufficient to identify the print as unique. The information is expressed in a 20-digit code. The fishbone method can be applied to fingerprint arches, records localized information, never runs out, and allows for graphical variation. The coding can be done by hand fairly quickly but is designed to be done by automatic scanners. The precise amount of coding to be done at each area of the print is determined by the type of use to which the codes are to be put. For a national single fingerprint collection, 30 digits from each visible delta and 20 from each core would be ample. For a loop, with one delta and one core, 50 digits would be recorded. For more complex patterns, possibly as many as 100 digits would be required. Graphic illustrations and 18 references are provided.