Graphs and richer property graphs are common models for real-world data. We typically run algorithms on such data to extract meaningful information. Using domainspecific programming languages (DSLs) is a common approach to expressing such algorithms, contrasting to general-purpose programming languages and declarative graph query languages. On one hand, algorithms in general-purpose languages are verbose and conceptually far removed from from the algorithm theory, as is the case for some community detection algorithms in DSLs. On the other hand, the DSLs that are available are insufficient to express all common graph analysis algorithms. The Green-Marl Intermediate Representation (GMIR) is such a graph algorithm DSL. As it has been built from the ground up, it only provides a minimal feature to support the algorithms it initially needed to support, similar to how other DSLs are developed. This specifically prevents frontier exploration algorithms and community detection algorithms to be expressed, such as Dijkstra’s shortest path and the Louvain clustering method. We use GMIR as a vehicle to introduce new domain-specific abstractions for algorithmic graph processing, targeting those algorithms. We evaluate our abstractions by implementing them in the commercial GMIR compiler, which we then use to compile various new algorithms to existing commercial graph processing platforms. This shows that we have successfully enabled more graph algorithms to be expressed in GMIR, even though there are still many algorithms that remain inexpressible.