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  "body": "\n## Summary\n\nIn the mathematical field of graph theory, the **intersection number** of a graph $G=(V,E)$ is the smallest number of elements needed to represent $G$ as an intersection graph of [[finite sets|070R982G4B]]. In such a representation, each vertex is represented as a set, and two vertices are connected by an edge whenever their sets have a common element. The intersection number equals the smallest number of [[cliques|0BYX1D7C2E]] (subgraphs with edges between all pairs of vertices) needed to cover all of the edges of $G$. Both this number and the computational problem of finding it have been studied under many alternative names.\n",
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