Degree distribution — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as orientation, preferential attachment, triangle counting — the same set of essays touches all of them, so they are one junction rather than several.
Two parameters are not enough either
Two graphs on 1,024 vertices with 3,072 edges each — identical in both numbers every bound in this field is written in. Enumerating every pair of neighbours of every vertex costs 18,480 examinations on one and 42,076 on the other. The quantity that separates them is a third parameter, it is computable in linear time, and it appears in no statement of the problem.
A bound right for the wrong reason
Orient every edge of a graph towards its higher-degree endpoint and count triangles among out-neighbours, and the work is O(E·d), where d is the graph's degeneracy. The usual reason given is that the orientation keeps every out-degree at most d. On a graph of 1,024 vertices with degeneracy four, 136 vertices have more than four out-neighbours and one has seven. The bound survives by a different argument, and the orientation that does keep every out-degree at most d does less work.
Named alongside it
The objects these essays reach for when they reach for this one.
Counted primitiveDegeneracyHonest limitMeasured countOrientationPreferential attachmentSparse graphTriangle countingComplexity classCounterexampleRegimeTwo parameter bound