  Graph state verification protocols allow multiple parties to share a graph
state while checking that the state is honestly prepared, even in the presence
of malicious parties. Since graph states are the starting point of numerous
quantum protocols, it is crucial to ensure that graph state verification
protocols can safely be composed with other protocols, this property being
known as composable security. Previous works [YDK21] conjectured that such a
property could not be proven within the abstract cryptography framework: we
disprove this conjecture by showing that all graph state verification protocols
can be turned into a composably secure protocol with respect to the natural
functionality for graph state preparation. Moreover, we show that any unchanged
graph state verification protocols can also be considered as composably secure
for a slightly different, yet useful, functionality. Finally, we show that
these two results are optimal, in the sense that any such generic result,
considering arbitrary black-box protocols, must either modify the protocol or
consider a different functionality.
  Along the way, we show a protocol to generalize entanglement swapping to
arbitrary graph states that might be of independent interest.
