Graph algorithms on distributed-memory systems typically perform heavy communication, often limiting their scalability and performance. This work presents an approach to transparently (without programmer intervention) allow fine-grained graph algorithms to utilize algorithmic communication reduction optimizations. In many graph algorithms, the same information is communicated by a vertex to its neighbors, which we coin algorithmic redundancy. Our approach exploits algorithmic redundancy to reduce communication between vertices located on different processing elements. We employ algorithm-aware coarsening of messages sent during vertex visitation, reducing both the number of messages and the absolute amount of communication in the system. To achieve this, the system structure is represented by a hierarchical graph, facilitating communication optimizations that can take into consideration the machine's memory hierarchy. We also present an optimization for small-world scale-free graphs wherein hub vertices (i.e., vertices of very large degree) are represented in a similar hierarchical manner, which is exploited to increase parallelism and reduce communication. Finally, we present a framework that transparently allows fine-grained graph algorithms to utilize our hierarchical approach without programmer intervention, while improving scalability and performance. Experimental results of our proposed approach on 131,000+ cores show improvements of up to a factor of 8 times over the non-hierarchical version for various graph mining and graph analytics algorithms.