DMGAE: An interpretable representation learning method for directed scale-free networks based on autoencoder and masking

Although existing graph self-supervised learning approaches have paid attention to the directed nature of networks, they have often overlooked the ubiquitous scale-free attributes. This oversight has resulted in a theoretical gap in understanding graph self-supervised learning from the perspective of network structure. In this paper, we study the degree distribution characteristics of source and target nodes in directed scale-free networks, encompassing node and edge dimensions. Our theoretical analysis reveals the relationship between the average degree of nodes and their average in-degree and out-degree, which is instrumental in discerning positive and negative edges, as well as edge directionality. Here positive edges are the ones that exists in the original graph, and negative edges are the ones that not exists in the original graph. Furthermore, we uncover negative edges connecting to central nodes and positive edges to peripheral nodes to be less predictable. Based on these crucial theoretical insights, we propose DMGAE (Directed Masked Graph Autoencoder), a novel representation learning method for directed scale-free networks that offers interpretability. The DMGAE method employs a weighted graph based on edges to replace the original graph structure. It integrates a masking approach based on the weight of the edges. Additionally, it incorporates an adaptive negative sampling method, edge decoder and a degree decoder based on the difference between the in-degree and out-degree of the node. This enhances the model’s capability to learn edges and discern their directions. Empirical studies on extensive real-world network data show that, compared to the state-of-the-art methods, DMGAE not only generally has superior learning performance on directed networks, but also performs exceedingly well on undirected networks.