  The intuitiveness of the tensor network graphical language is becoming well
known through its use in numerical simulations using methods from tensor
network algorithms. Recent times have also seen rapid progress in developing
equations of motion to predict the time evolution of quantum entanglement
[Nature Physics, 4(\textbf{4}):99, 2008]. Here we cast these recent results
into a tensor network framework and in doing so, construct a theory which
exposes the topological equivalence of the evolution of a family of
entanglement monotones in arbitrary dimensions. This unification was
accomplished by tailoring a form of channel state duality through the
interpretation of graphical tensor network rewrite rules. The introduction of
tensor network methods to the theory of entanglement evolution opens the door
to apply methods from the rapidly evolving area known as tensor network states.
