Analytical hardware performance models yield swift estimation of desired hardware performance metrics. However, developing these analytical models for modern processors with sophisticated microarchitectures is an extremely laborious task and requires a firm understanding of target microarchitecture's internal structure. In this paper, we introduce GRANITE, a new machine learning model that estimates the throughput of basic blocks across different microarchitectures. GRANITE uses a graph representation of basic blocks that captures both structural and data dependencies between instructions. This representation is processed using a graph neural network that takes advantage of the relational information captured in the graph and learns a~rich neural representation of the basic block that allows more precise throughput estimation. Our results establish a new state-of-the-art for basic block performance estimation with an average test error of 6.9% across a wide range of basic blocks and microarchitectures for the x86-64 target. Compared to recent work, this reduced the error by 1.7% wile improving training and inference throughput by approximately 3.0x. In addition, we propose the use of multi-task learning with independent multi-layer feed forward decoder networks. Our results show that this technique further improves precision of all learned models while significantly reducing per-microarchitecture training costs. We perform an extensive set of ablation studies and comparisons with prior work, concluding a set of methods to achieve high accuracy for basic block performance estimation.