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  "body": "\n## Definition\n\nA *geometric graph* is a pair $(V, E)$ such that:\n\n1. $V$ is a finite set of points in $\\R^2$ in general position, that is, no three of them lie on a common line;\n2. $E$ is a set of closed [[line segments|VQ4Q2V45RP]] each of whose two endpoints lie in $V$.\n\nThe points of $V$ are its vertices and the segments of $E$ are its edges.\nIts underlying abstract [[graph|00C0BR7D7H]] has vertex set $V$, with $u$ and $v$ adjacent when the segment from $u$ to $v$ is in $E$.\nTwo edges cross if they meet at a point that is not a common endpoint.\n\n## Remarks\n\nExample: let $V$ be the four points $(0,0)$, $(1,0)$, $(1,1)$, $(0,1)$ and let $E$ be all six segments between them.\nNo three of these points are collinear and every segment has its endpoints in $V$, so this is a geometric graph.\nIts underlying graph is $K_4$, and the two diagonals cross at $(1/2, 1/2)$.\n\nNon-example: the points $(0,0)$, $(1,0)$, $(2,0)$ with the segment from $(0,0)$ to $(2,0)$ fail clause 1, since the three points are collinear, and the segment passes through a third vertex.\n\nA geometric graph is called plane when no two of its edges cross.\nSome authors drop the general position condition and only require that no edge passes through a vertex other than its endpoints.\n",
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