A weight system of degree 
for framed knots is a linear
functional on the degree-
component of an algebra
of chord diagrams. Here 
is a nonnegative integer,
and the scalars may be taken in the rational numbers
or real numbers. Equivalently, it assigns a scalar
to each degree-
chord diagram, subject to the four-term
relations (Bar-Natan 1995, author version, pp. 4, 6).
For unframed knots, the one-term relation is imposed as well. Thus a framed weight system can be nonzero on a diagram with an isolated chord, whereas an unframed weight system cannot.
Over the real numbers, a Vassiliev invariant of degree 
determines a degree-
weight system recording its highest-degree part. Unframed weight systems of degree
form the dual
vector space of the degree-
unframed algebra of
chord diagrams. The Kontsevich integral
realizes them as highest-degree parts of Vassiliev
invariants (Bar-Natan 1995, author version, pp. 4-5).
