Hypergraph theory was developed from graph theory. In a graph, an edge can only connect two vertices, while in a hypergraph, an edge can connect more than two vertices. One problem that is more accurately described with a hypergraph is the problem of complex networks of proteins. This study examines the matrix analysis of a complete tripartite hypergraph using an equitable partition technique. The results of this matrix study are then used to facilitate the modeling of problems related to the hypergraph. One of the problems modeling studies with a complete tripartite hypergraph is Folksonomies, namely a classification system in which end users apply public tags to online items.