Fig. 1. Overview of DNE.

(A) DNE comprises three main steps: (i) initializing nodes using Laplacian eigenvectors (LEs) of the network’s adjacency matrix, optionally concatenated with node features when available; (ii) identifying node neighbors as positive nodes via stochastic neighbors selection and selecting nodes from other network regions as negative nodes, based on the distribution of node degrees; and (iii) embedding each node through a deep learning encoder, optimizing the encoder’s parameters to ensure the node embeddings preserve discrimination between neighboring and nonlocal nodes. (B) Utilization of the pretrained encoder to generate node representations for versatile downstream analysis tasks.