Say I have a graph $G$ which has edges colored with colors red and blue. Let's call this coloring $C$. Is there a way I can say that one coloring is closer to $C$ compared to another? Perhaps saying it is easier to reach from one coloring of a graph to $C$ compared to another coloring of a graph.
For example, if let's call it $A$ if all edges are colored red, $B$ if all the edges are colored blue, and $C$ is the coloring which has all edges blue except one, which is red. This $C$ is obviously closer to $B$ than $A$ in some sense.
Can I quantify it?