The title sums it up pretty succinctly; I'm trying to visualize the search space of the traveling salesman problem, and I was wondering if there is any way to visually represent the search space as neighbors of each other in 2D.
For example, if you had the TSP with four $3$ cities, you could list all the combinations as $1-2-3, 2-1-3, 3-2-1, 1-3-2, 2-3-1, 3-1-2$, but is there an established way to represent them on a grid with a relation to each other? Unfortunately searching doesn't seem to turn up many answers.
There are multiple ways, as a graph, as a relation between the set of vertices with itself; in the form of a subset of the Cartesian product. etc. $$1\leftarrow2\leftarrow3$$ this is a directed graph for example. Where as :$$\begin{array}{cccc}3&&&\\2&&&\color{red}{\blacksquare}\\1&&\color{red}{\blacksquare}&\\&1&2&3\end{array}$$
is a representation on a Cartesian product of the relation "is directionally connected to". Higher dimensional graphs of all possible relations, would take putting the next lowest Cartesian product's tuples as one of the co-ordinates. But, I doubt it's truely conventionalized.