Editing De Bruijn sequence (section)

===Example using de Bruijn graph===
[[File:de_Bruijn_binary_graph.svg|thumb|300px|Directed graphs of two ''B''(2,3) de Bruijn sequences and a ''B''(2,4) sequence. In ''B''(2,3), each vertex is visited once, whereas in ''B''(2,4), each edge is traversed once.]]

Goal: to construct a ''B''(2,&nbsp;4) de Bruijn sequence of length 2<sup>4</sup> = 16 using Eulerian (''n''&nbsp;−&nbsp;1 = 4&nbsp;−&nbsp;1 = 3) 3-D de Bruijn graph cycle.

Each edge in this 3-dimensional de Bruijn graph corresponds to a sequence of four digits: the three digits that label the vertex that the edge is leaving followed by the one that labels the edge. If one traverses the edge labeled 1 from 000, one arrives at 001, thereby indicating the presence of the subsequence 0001 in the de Bruijn sequence.  To traverse each edge exactly once is to use each of the 16 four-digit sequences exactly once.

For example, suppose we follow the following Eulerian path through these vertices:

:000, 000, 001, 011, 111, 111, 110, 101, 011,

::110, 100, 001, 010, 101, 010, 100, 000.

These are the output sequences of length ''k'':

:0 0 0 0
:_ 0 0 0 1
:_ _ 0 0 1 1

This corresponds to the following de Bruijn sequence:

:0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1

The eight vertices appear in the sequence in the following way:

       {0  0  0  0} 1  1  1  1  0  1  1  0  0  1  0  1
        0 {0  0  0  1} 1  1  1  0  1  1  0  0  1  0  1
        0  0 {0  0  1  1} 1  1  0  1  1  0  0  1  0  1
        0  0  0 {0  1  1  1} 1  0  1  1  0  0  1  0  1
        0  0  0  0 {1  1  1  1} 0  1  1  0  0  1  0  1
        0  0  0  0  1 {1  1  1  0} 1  1  0  0  1  0  1
        0  0  0  0  1  1 {1  1  0  1} 1  0  0  1  0  1
        0  0  0  0  1  1  1 {1  0  1  1} 0  0  1  0  1
        0  0  0  0  1  1  1  1 {0  1  1  0} 0  1  0  1
        0  0  0  0  1  1  1  1  0 {1  1  0  0} 1  0  1
        0  0  0  0  1  1  1  1  0  1 {1  0  0  1} 0  1
        0  0  0  0  1  1  1  1  0  1  1 {0  0  1  0} 1
        0  0  0  0  1  1  1  1  0  1  1  0 {0  1  0  1}
        0} 0  0  0  1  1  1  1  0  1  1  0  0 {1  0  1 ...
    ... 0  0} 0  0  1  1  1  1  0  1  1  0  0  1 {0  1 ...
    ... 0  0  0} 0  1  1  1  1  0  1  1  0  0  1  0 {1 ...

...and then we return to the starting point.  Each of the eight 3-digit sequences (corresponding to the eight vertices) appears exactly twice, and each of the sixteen 4-digit sequences (corresponding to the 16 edges) appears exactly once.