[titzer]

I generally concur. Compilers that do advanced optimizations represent both control flow and data flow of the program as a graph where the nodes can represent basic blocks or operations in the program. One of the most graph-like IRs is called the "sea of nodes" and literally represents the entire program as a directed graph of nodes and edges that represent dependencies. Most compiler programs amount to traversing, matching, and transforming one or more nodes at a time. Graph coloring itself (i.e. the graph coloring problem) is often used to solve register allocation, a key optimization needed to make efficient use of the fastest storage in modern computers, the register file. Graph coloring works on a different representation of the program called the Interference Graph, where nodes represent variables and edges represent interferences. Graph coloring for general graphs is NP-complete, so heuristics are used.

So yes, I mostly concur. Compiler algorithms are usually graph algorithms.