In recent years, many excellent computational models have emerged in microbe-drug association prediction, but their performance still has room for improvement. This paper proposed the OGNNMDA framework, which applied an ordered message-passing mechanism to distinguish the different neighbor information in each message propagation layer, and it achieved a better embedding ability through deeper network layers. Firstly, the method calculates four similarity matrices based on microbe functional similarity, drug chemical structure similarity, and their respective Gaussian interaction profile kernel similarity. After integrating these similarity matrices, it concatenates the integrated similarity matrix with the known association matrix to obtain the microbe-drug heterogeneous matrix. Secondly, it uses a multi-layer ordered message-passing graph neural network encoder to encode the heterogeneous network and the known association information adjacency matrix, thereby obtaining the final embedding features of the microbe-drugs. Finally, it inputs the embedding features into the bilinear decoder to get the final prediction results. The OGNNMDA method performed comparative experiments, ablation experiments, and case studies on the aBiofilm, MDAD and DrugVirus datasets using 5-fold cross-validation. The experimental results showed that OGNNMDA showed the strongest prediction performance on aBiofilm and MDAD and obtained sub-optimal results on DrugVirus. In addition, the case studies on well-known drugs and microbes also support the effectiveness of the OGNNMDA method. Source codes and data are available at: https://github.com/yyzg/OGNNMDA.

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