Binary code similarity detection is an important problem with applications in areas like malware analysis, vulnerability research and plagiarism detection. This paper proposes a novel graph neural network architecture combined with a novel graph data representation called call graphlets. A call graphlet encodes the neighborhood around each function in a binary executable, capturing the local and global context through a series of statistical features. A specialized graph neural network model is then designed to operate on this graph representation, learning to map it to a feature vector that encodes semantic code similarities using deep metric learning. The proposed approach is evaluated across four distinct datasets covering different architectures, compiler toolchains, and optimization levels. Experimental results demonstrate that the combination of call graphlets and the novel graph neural network architecture achieves state-of-the-art performance compared to baseline techniques across cross-architecture, mono-architecture and zero shot tasks. In addition, our proposed approach also performs well when evaluated against an out-of-domain function inlining task. Overall, the work provides a general and effective graph neural network-based solution for conducting binary code similarity detection.