A line digraph $L(G) = (A, E)$ is the digraph constructed from the digraph $G = (V, A)$ such that there is an arc $(a,b)$ in $L(G)$ if the terminal node of $a$ in $G$ is the initial node of $b$. The maximum number of arcs in a line digraph with $m$ nodes is $(m/2)^2 + (m/2)$ if $m$ is even, and $((m - 1)/2)^2 + m - 1$ otherwise. For $m \geq 7$, there is only one line digraph with as many arcs if $m$ is even, and if $m$ is odd, there are two line digraphs, each being the transpose of the other.

翻译：有向线图 $L(G) = (A, E)$ 是由有向图 $G = (V, A)$ 构造而成的有向图，其中当 $a$ 在 $G$ 中的终止节点是 $b$ 的起始节点时，$L(G)$ 中存在弧 $(a,b)$。具有 $m$ 个节点的有向线图的最大弧数，当 $m$ 为偶数时为 $(m/2)^2 + (m/2)$，否则为 $((m - 1)/2)^2 + m - 1$。对于 $m \geq 7$，当 $m$ 为偶数时，仅存在一个具有最多弧数的有向线图；当 $m$ 为奇数时，则存在两个这样的有向线图，且二者互为转置。