  Quantum teleportation plays a key role in modern quantum technologies. Thus,
it is of much interest to generate alternative approaches or representations
aimed at allowing us a better understanding of the physics involved in the
process from different perspectives. With this purpose, here an approach based
on graph theory is introduced and discussed in the context of some
applications. Its main goal is to provide a fully symbolic framework for
quantum teleportation from a dynamical viewpoint, which makes explicit at each
stage of the process how entanglement and information swap among the qubits
involved in it. In order to construct this dynamical perspective, it has been
necessary to define some auxiliary elements, namely virtual nodes and edges, as
well as an additional notation for nodes describing potential states (against
nodes accounting for actual states). With these elements, not only the flow of
the process can be followed step by step, but they allow us to establish a
direct correspondence between this graph-based approach and the usual state
vector description. To show the suitability and versatility of this graph-based
approach, several particular teleportation examples are examined, which include
bipartite, tripartite and tetrapartite maximally entangled states as quantum
channels. From the analysis of these cases, a general protocol is discussed in
the case of sharing a maximally entangled multi-qubit system.
