A chord diagram of degree 
,
where 
is a nonnegative integer, is an oriented circle with 
distinct marked points partitioned
into 
pairs, considered up to orientation-preserving reparameterization of the circle.
The pairs are represented by chords. The interior intersections
of the drawn chords are not additional marked points
(Bar-Natan 1995).
The diagram records the cyclic order of the paired points, not their distances
or the shape of the drawn chords. The degree-zero diagram
is an oriented circle with no marked points.
For a singular knot with 
ordinary double points,
pairing the two points in the preimage
of each ordinary double point gives a chord
diagram of degree 
.
Chord diagrams occur in the algebra of chord diagrams and the theory of Vassiliev invariants.
