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Graph data is essential for modeling complex relationships among entities. Graph Neural Networks (GNNs) have demonstrated effectiveness in processing low-order undirected graph data; however, in complex directed graphs, relationships between nodes extend beyond first-order connections and encompass higher-order relationships. Additionally, the asymmetry introduced by edge directionality further complicates node interactions, presenting greater challenges for extracting node information. In this paper, We propose TWC-GNN, a novel graph neural network design, as a solution to this problem. TWC-GNN uses node degrees to define higher-order topological structures, assess node importance, and capture mutual interactions between central nodes and their adjacent counterparts. This approach improves our understanding of complex relationships within the network. Furthermore, by integrating self-attention mechanisms, TWC-GNN effectively gathers higher-order node information in addition to focusing on first-order node information. Experimental results demonstrate that the integration of topological structures and higher-order node information is crucial for the learning process of graph neural networks, particularly in directed graphs, leading to improved classification accuracy. [ABSTRACT FROM AUTHOR]