A balanced hypergraph is a specific type of hypergraph that meets certain criteria in relation to the sizes of its hyperedges. In hypergraphs, an edge (or hyperedge) can connect any number of vertices, unlike traditional graphs where an edge connects exactly two vertices. A hypergraph is considered balanced if it satisfies the following property: - **Uniform Edge Size**: All hyperedges in the hypergraph must have the same size, say \( k \).

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