Bipartite hypergraph

Okay, first let's talk about a regular graph. You know when we draw a graph with circles (we call them nodes) and lines (we call them edges) connecting them? Well, a regular graph has only two kinds of things - nodes and edges - and each edge connects exactly two nodes.

Now, a hypergraph is like a graph, but instead of each edge connecting two nodes, it can connect as many nodes as we want. So we might have a hypergraph with a bunch of nodes, and some edges that connect three of them, some edges that connect four of them, and so on.

Finally, a bipartite hypergraph is a hypergraph where we can split all the nodes into two groups, let's call them A and B, so that every edge connects some nodes from A and some nodes from B. In other words, we can draw all the nodes as either circles all on the left side, or circles all on the right side, and connect them with lines, but we'll never have a line that crosses over from the left side to the right side.

So basically, a bipartite hypergraph is a special kind of hypergraph where we can cleanly split all the nodes into two groups, and every edge connects some nodes from each group.