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Aggregation functions are regarded as the multiplication between an aggregation matrix and node embeddings, based on which a full rank matrix can enhance representation capacity of Graph Neural Networks (GNNs). In this work, we fill this research gap based on the full rank aggregation matrix and its functional form, i.e., the injective aggregation function, and state that injectivity is necessary to guarantee the rich representation capacity to GNNs. To this end, we conduct theoretical injectivity analysis for the typical feature aggregation methods and provide inspiring solutions on turning the non-injective aggregation functions into injective versions. Based on our injective aggregation functions, we create various GNN structures by combining the aggregation functions with the other ingredient of GNNs, node feature encoding, in different ways. Following these structures, we highlight that by using our injective aggregation function entirely as a pre-processing step before applying i

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