Cataloging graphs by generating them uniformly at random
Adalbert Kerber, Reinhard Laue, R. W. Hager, W. Weber · Journal of Graph Theory · 1990
Abstract We describe an algorithm for cataloging graphs by generating them uniformly at random. The method used is based on a recent algorithm by Dixon and Wilf that generates orbit representatives uniformly at random. The approach is refined to graphs with prescribed numbers of edges and vertices, and then applied to obtain the complete list of graphs on 10 vertices.