Changing the topology of Tensor Networks

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.