De Bruijn graph
In graph theory, an formula_1-dimensional De Bruijn graph of formula_2 symbols is a directed graph representing overlaps between sequences of symbols. It has formula_3 vertices, consisting of all possible length-formula_1 sequences of the given symbols; the same symbol may appear multiple times in a sequence. For a set of formula_2 symbols formula_6, the set of vertices is:
formula_7

If one of the vertices can be expressed as another vertex by shifting all its symbols by one place to the left and adding a new symbol at the end of this vertex, then the latter has a directed edge to the former vertex. Thus the set of arcs (that is, directed edges) is
formula_8

Although De Bruijn graphs are named after Nicolaas Govert de Bruijn, they were discovered independently by both De Bruijn and I. J. Good. Much earlier, Camille Flye Sainte-Marie implicitly used their properties.
Q131476
graph theory
Concept
Q1137726
directed graph
Concept
Q1304193
vertices
Concept
Q1078285
Nicolaas Govert de Bruijn
PER
Q224372
I. J. Good
PER
Q3066095
De Bruijn graph
MEDIA
Q3066095
De Bruijn graph
MEDIA
+1^^http://www.w3.org/2001/XMLSchema#decimal
1
NUMBER
+2^^http://www.w3.org/2001/XMLSchema#decimal
2
NUMBER
+3^^http://www.w3.org/2001/XMLSchema#decimal
3
NUMBER
+1^^http://www.w3.org/2001/XMLSchema#decimal
1
NUMBER
+2^^http://www.w3.org/2001/XMLSchema#decimal
2
NUMBER
+6^^http://www.w3.org/2001/XMLSchema#decimal
6
NUMBER
+7^^http://www.w3.org/2001/XMLSchema#decimal
7
NUMBER
+8^^http://www.w3.org/2001/XMLSchema#decimal
8
NUMBER
studies
subclass of
named after
studies