  In many applications, it is needed to change the topology of a tensor network
directly and without approximation. This work will introduce a general scheme
that satisfies these needs. We will describe the procedure by two examples and
show its efficiency in terms of memory consumption and speed in various
numerical experiments. In general, we are going to provide an algorithm to add
an edge to a tensor network as well as an algorithm to remove an edge unless
the resulting network is a connected graph.
