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We examine two greedy heuristics - wiring and rewiring - for constructingmaximum assortative graphs over all simple connected graphs with a targetdegree sequence. Counterexamples show that natural greedy rewiring heuristicsdo not necessarily return a maximum assortative graph, even though it is knownthat the meta-graph of all simple connected graphs with given degree isconnected under rewiring. Counterexamples show an elegant greedy graph wiringheuristic from the literature may fail to achieve the target degree sequence ormay fail to wire a maximally assortative graph.

Common greedy wiring and rewiring heuristics do not guarantee maximum assortative graphs of given degree