Using the concept of linkage of closed loops to determine topological invariants of a cutting graph

The calculation of time varying electromagnetic fields requires that the topological connectivity of conducting material be known in order to ensure that a magnetic scalar potential is well defined. The intersection of cutting surfaces with a multiply connected conducting region forms looplike components of a cutting graph. It is shown that it is possible to distinguish these components by determining a measure for the linkage of loops in the space surrounding the conductor.<>