Informally, hypergraph is a generalization of a graph in which an edge can join any number of vertices.
A hypergraph $G=(V, E)$ is a two tuple, where $V$ is the set of vertices and $E$ is a set contain subsets of the vertex set of $V$. An example of hyper-graph is given below and for example edge $e_3$ is a subset contain $v_3,v_5,v_6$ and similarly for other edges.
Isomorphism : Two hyper graphs $G(V,E)$ and $H(V,E')$ are isomorphic if there is a permutation $g$ on $V$ such that, $\forall $ $e \in E$, $$e\in E \iff g(e) \in E'$$
Question : Is the hypergraph isomorphism preserve the size of edge (edge is a subset of vertex set here) i.e. an edge $e$ that contain say $l$ vertices will be mapped to edge $g(e)$ whose size is also $l$ or it is not required.