The word "at least" here deserves special attention: for every link L we need to obtain its regular (or generic) shadow- a shadow without catastrophes, singularities, or degenerations. Let L be a polygonal link. Its shadow L' is regular if the following conditions are satisfied: 

1. the shadow is a 4-valent (or 4-regular) graph; 
2. if Q' is a point in L', then the inverse image p^-1(Q' )ÇL has at most two points. If it has two points, they must be the interior points of two distinct edges of L, and Q' is the vertex (or crossing) in L'. Otherwise, Q' can have only one inverse image. 

This means that every vertex of a shadow will be 4-valent, two or more vertices of the polygonal link L cannot be projected to the same point, any vertex (or several vertices) of L cannot fall on the projection of an edge or line segment (to which they don't belong), three or more points cannot be projected to the same point, and projections of different edges of L or their parts cannot coincide in L'. The forbidden situations can be removed by a suitable choice of projection plane and by slightly displacing one of the vertices of the polygonal link L. As with any other graph, a shadow of a KL can be given by a list of unordered pairs, or by an adjacency matrix, but complete information from which you can draw it is given by the code of planar embedding of that graph. 

From the point of view of graph theory, the result obtained, the link shadow L', is a 4-valent (or 4-regular) plane graph. We will try to find which information about the original link L can be recovered from it.