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Network alignment techniques that map the same entities across multiple networks assume that the mapping nodes in two different networks have similar attributes and neighborhood proximity. However, real-world networks often violate such assumptions, having diverse attributes and structural properties. Node mapping across such structurally heterogeneous networks remains a challenge. Although capturing the nodes’ entire neighborhood (in low-dimensional embeddings) may help deal with these characteristic differences, the issue of over-smoothing in the representations that come from higherorder learning still remains a major problem. To address the above concerns, we propose SAlign: a supervised graph neural attention framework for aligning structurally heterogeneous networks that learns the correlation of structural properties of mapping nodes using a set of labeled (mapped) anchor nodes. SAlign incorporates nodes’ graphlet information with a novel structure-aware cross-network attention mechanism that transfers the required higher-order structure information across networks. The information exchanged across networks helps in enhancing the expressivity of the graph neural network, thereby handling any potential over-smoothing problem. Extensive experiments on three real datasets demonstrate that SAlign consistently outperforms the state-of-the-art network alignment methods by at least 1.3-8% in terms of accuracy score. The code is available at https://github.com/shruti400/SAlign for reproducibility.