  It is known that context-free grammars can be extended to generating graphs
resulting in graph grammars; one of such fundamental approaches is hyperedge
replacement grammars. On the other hand there are type-logical grammars which
also serve to describe string languages. In this paper, we investigate how to
extend the Lambek calculus ($\mathrm{L}$) and grammars based on it to graphs.
The resulting approach is called hypergraph Lambek calculus ($\mathrm{HL}$). It
is a logical sequential calculus whose sequents are graphs; it naturally
extends the Lambek calculus and also allows one to embed its variants
(commutative $\mathrm{L}$, $\mathrm{NL\diamondsuit}$,
$\mathrm{L}_{\mathbf{1}}^\ast$). Besides, many properties of the Lambek
calculus (cut elimination, counters, models) can be lifted to $\mathrm{HL}$.
However, while Lambek grammars are equivalent to context-free grammars in the
string case, hypergraph Lambek grammars are much more powerful than hyperedge
replacement grammars. Particularly, the former can generate the language of all
graphs without isolated nodes; the language of all bipartite graphs; finite
intersections of languages generated by hyperedge replacement grammars.
Nevertheless, the derivability problem in $\mathrm{HL}$ and the membership
problem for grammars based on $\mathrm{HL}$ are NP-complete as well as the
membership problem for hyperedge replacement grammars.
