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We propose a new method for obtaining complete asymptotic expansions in asystematic manner, which is suitable for counting sequences of various graphfamilies in dense regime. The core idea is to encode the two-dimensional arrayof expansion coefficients into a special bivariate generating function, whichwe call a coefficient generating function. We show that coefficient generatingfunctions possess certain general properties that make it possible to expressasymptotics in a short closed form. Also, in most scenarios, we indicate acombinatorial meaning of the involved coefficients. Applications of our methodinclude asymptotics of connected graphs, irreducible tournaments, stronglyconnected digraphs, satisfiable 2-SAT formulae and contradictory stronglyconnected implication digraphs. Moreover, due to its flexibility, the methodallows to treat a wide range of structural variations, including fixing thenumbers of connected, irreducible, strongly connected and contradictorycomponents, having the variations on source-like, sink-like and isolatedcomponents, or adding weights and marking variables.

Asymptotics for graphically divergent series: dense digraphs and 2-SAT formulae