The Petersen graph was constructed by Kempe as the graph whose vertices correspond to the points of the Desargues configuration and edges to pairs of points that do not lie on lines that are part of the configuration. The graph at right corresponds to this construction and, though not immediately apparent from its embedding, it is in fact isomorphic to the Petersen graph. Graphs produced from configurations in this way have been termed ordinary (line) graphs by Ed Pegg, Jr. as a result of the fact that the edges of such graphs correspond to ordinary lines of the underlying configuration.

configuration | ordinary line | Petersen graph