Linking number

In mathematics, the linking number is an invariant which describes the entanglement of two non- interpenetrating, closed curves in three-dimensional space. The linking number is always an integer and can be positive or negative depending on the orientation ( flow direction) of the curves. Intuitively, the linking number, the number of turns around each of the curves dar.

Calculation of the linking number

We consider two closed curves and is given for each orientation ( direction of passage ). The linking number of and is defined by the number of positive and negative crossings and in an entanglement graph as follows (see Figure for the convention for positive and negative crossings):