The degeneracy of a graph is the maximum degree of all vertices in any subgraph of G. This is essentially equivalent to the coloring number of G, which is the least number k such that there exists an ordering of the vertices of G in which each vertex has less than k neighbors earlier in the ordering. The coloring number is equal to the degeneracy plus one.
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The object degeneracy is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Graphs.m2:3293:0.