A hypergraph is a graph where an edge (called a hyperedge or link) may connect multiple vertices (a subset of the vertex set, to be exact). A matrix representation for such a graph is an v ×e matrix,...

A hypergraph is a graph where an edge (called a hyperedge or link) may connect multiple vertices (a subset of the vertex set, to be exact). A matrix representation for such a graph is an v ×e matrix, where v is the number of vertices, e is the number of links, and an entry (i, j) corresponds to edge j being incident on vertex i.

(a) Given a hypergraph with n vertices, m edges and with matrix representation M, what are the dimensions of MMT ? What about MTM?

(b) What does this say about using neighborhood-based kernels on vertices of hypergraphs? Is there anything to be worried about?