Abstract We examine two greedy heuristics — wiring and rewiring — for constructing maximum assortative graphs over all simple connected graphs with a target degree sequence. Counterexamples show that natural greedy rewiring heuristics do not necessarily return a maximum assortative graph, even though it is known that the meta-graph of all simple connected graphs with given degree is connected under rewiring. Counterexamples show an elegant greedy graph wiring heuristic from the literature may fail to achieve the target degree sequence or may fail to wire a maximally assortative graph.
We report the current state of the graph isomorphism problem from the practical point of view. After describing the general principles of the refinement-individualization paradigm and pro ving its validity, we explain how it is implemented in several of the key implementations. In particular, we bring the description of the best known program nauty up to date and describe an innovative approach called Traces that outperforms the competitors for many difficult graph classes. Detailed comparisons against saucy, Bliss and conauto are presented.