The LinKnot function fDowCodes (webMathematica fDowCodes) calculates all Dowker codes of KLs realizable in the plane Â2 (or on the sphere S3). Beginning from a set {2,4,...,2n}, it calculates all its distinct permutations, produces for each them all possible choices of components (by using all partitions of the permutations mentioned), creates their corresponding KLs, and checks their realizability by using Dowker-Thistlethwaite algorithm (Dowker and Thistlethwaite, 1983), extended to links by H. Doll and J. Hoste (1991)

From a shadow of a KL we can create another plane graph- a graph of a link, in the following way: first color every other region of the KL shadow black or white, so that the infinite outermost region is black. In the chess-board coloring (or Tait coloring) of the plane obtained, put a vertex at the center of each white region. Then connect any two vertices that are in regions that share a crossing with an edge containing that crossing. The result obtained is the graph of the KL corresponding to a particular KL shadow. There is a one-to-one correspondence between KL shadows and graphs of KLs. 

The LinKnot function fGraphKL (webMathematica fGraphKL) calculates and draws a graph of any given KL. The output is a graph of a KL given by the list of unordered pairs and its drawing.