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.

For the particularly useful subgraph of topics, see "Notes on Graph Algorithms Used in Optimizing Compilers" by Carl Offner: http://www.cs.umb.edu/~offner/files/flow_graph.pdf

That, and pretty much anything (co)authored by Robert E. Tarjan. I'm serious: https://github.com/search?q=repo%3Allvm%2Fllvm-project%20tar...

There's a good recent survey of the three workhorses: "We survey three algorithms that use depth-first search to find the strong components of a directed graph in linear time: (1) Tarjan's algorithm; (2) a cycle-finding algorithm; and (3) a bidirectional search algorithm."

Finding Strong Components Using Depth-First Search Robert E. Tarjan, Uri Zwick https://arxiv.org/abs/2201.07197

Control flow and data flow of programs are modelled as graphs so that certain analysis and transformations can be applied. That involves subgraph similarities, graph searches, graph transformation rules etc. And at the tail end, register allocation is graph coloring. Check out the LLVM and MLIR projects if you want some concrete modern examples.