A linear hypergraph is a hypergraph in which any two distinct hyperedges intersect in at most one graph vertex. Equivalently, no pair of vertices is contained in two different hyperedges. Every simple ordinary graph, regarded as a 2-uniform hypergraph, is linear.
Linear hypergraphs play a role in hypergraph versions of extremal graph theory and spectral graph theory. In particular, Dong et al. (2026)
give upper bounds on the spectral radii of Berge
-free linear 
-uniform hypergraphs for 
and 
.
-Free
Linear 
-Graphs."
Electron. J. Combin. 33, P3.82, 2026.