{
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  "body": "\n## Summary\n\nIn graph theory, the **bipartite half** or **half-square** of a [[bipartite graph|07DVHJ8N0A]] $G = (U,V,E)$ is a [[graph|00C0BR7D7H]] whose vertex set is one of the two sides of the bipartition (without loss of generality, $U$) and in which there is an edge $u_{i}u_{j}$ for each pair of vertices $u_{i}, u_{j}$ in $U$ that are at [[distance|0QV9VNNB4Z]] two from each other in $G$. That is, in a more compact notation, the bipartite half is $G^{2}[U]$ where the superscript 2 denotes the square of a graph and the square brackets denote an [[induced subgraph|0EREPBVG2G]].\n",
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        "what": "edge defines in",
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        "what": "edge instance_of in",
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