In multiparty session types, interconnection networks identify
which roles in a session engage in direct communication. If role
p is connected to role q, then p exchanges a message with q.
In a session-based interpretation of classical linear logic (CLL),
this corresponds to the composition, or cut, of dual propositions.
This paper shows that well-formed interactions represented in a
session-based interpretation of CLL form strictly less expressive
interconnection networks than those specified in a multiparty session
calculus. To achieve this, we introduce a new compositional
synthesis property, dubbed partial multiparty compatibility (PMC),
enabling us to build a global type denoting the interactions obtained
by iterated composition of well-typed CLL processes.We show that
the CLL composition rule induces PMC global types without circular
interconnections between three participants. PMC is then used
to define a new CLL multicut rule which can form general multiparty
interconnections, preserving the deadlock-freedom property
of CLL.