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For an alphabet of size $q$, the order-$n$ directed graph has words of length $n-1$ as vertices and words of length $n$ as edges. An edge goes from its prefix of length $n-1$ to its suffix of that length. An Eulerian cycle therefore lists every length-$n$ word once as a cyclic window, producing a De Bruijn sequence.

A cyclic sequence over an alphabet of size $q$ in which every word of length $n$ appears exactly once as a cyclic window. Its length is $q^n$. The De Bruijn graph converts its construction into an Eulerian cycle problem.