Function Notation

I write $f(x)$ for the node you reach from node $x$ in one step. If node $3$ points to node $7$, then $f(3) = 7$. This notation comes from viewing the graph as a function. The graph is functional because $f$ is a function. Every input has exactly one output.

No node has zero edges or two edges. This notation makes composition natural: $f(f(x))$ means two steps from $x$, written as $f^2(x)$. In general, $f^k(x)$ means $k$ steps from $x$. Powers of $f$ let you talk about paths concisely.