Component Algorithm  Let us choose as a beginning point any vertex x of L', and any oriented edge (x,y) incident to it. After coming to vertex y, we choose the middle of the three remaining edges and orient it so that its beginning point is y. Continuing to apply that rule, we will close a first circuit. It is a shadow of one component of L. After that, we choose another vertex (the same or different from the first) incident to at least one edge not used before, and we start from that edge. We continue to apply the same algorithm until all the edges of the graph are exhausted.
 

After tracing all circuits in L' we obtain the first and simplest KL invariant- the component number c. On the other hand, from every 4-valent plane graph L' we can obtain a link L, such that L' is a shadow of L, and the number of circuits c in L obtained by the Component Algorithm is the number of components of L. 

The LinKnot function fComponentNo (webMathematica fComponentNo) calculates the number of components of any KL

In the existing KL tables, all KLs are strongly divided into separate classes, according to the number of components. In our discussion, we will try to work with all of them together far as it is possible, trying to find some order in the complete set of KLs and make their classification. 
 
 

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