On the Second Eigenvalue of Hypergraphs

where n = |V |. Let G = (V,E) be a 3-uniform hypergraph; i.e. E is a subset of subsets of V of size 3. We consider the space, L(V ), of real valued functions on V with the usual inner product; let e1, . . . , en be the standard basis for L(V ), where ei takes the value 1 on the i-th vertex of V and 0 elsewhere. It is natural to construct from G a trilinear form, that is a map from τ , mapping triples of vectors in L(V ) to R, namely τ  n ∑