I've already understood the basic nomenclature for knot and links, especially links consisting trivial knots (circle). However, things got much complicated when I was working on the case when circles are replaced by 2-bouquet graphs (which may be regarded homotopic to two circle glued together). For example, how do you name these links below by link diagrams or projections? enter image description here
And further, how could I find out their linking numbers?
In fact, you can use some kind of "homotopy trick"here. As this example is clearly easy to avoid further confusion, there is an approach to compute linking numbers for simple graphs without complicated intra- or interwoven feature: (linking number of graphs) The linking number λ(G) of a graph G is: $ λ(G) = ∑_{i=j} λ(G_i, G_j)$,
where $λ(G_i,G_j) = ∑|λ(z_p,z_q)|$ for ball basis cycles $z_p,z_q$ in different components $G_i,G_j$,respectively.
The linking number is computed only between pairs of components following Seifert’s original definition. Linked cycles within the same component may be unlinked by a homotopy (Prasolov, 1995).
REF: 1 Prasolov, V. V., & Prasolov, V. V. E. (1995). Intuitive topology (No. 4). American Mathematical Soc..