Understanding and quantifying node importance is a fundamental problem in network science and engineering, underpinning a wide range of applications such as influence maximization, social recommendation, and network dismantling. Prior research often relies on centrality measures or advanced graph embedding techniques using structural information, followed by downstream classification or regression tasks to identify critical nodes. However, these approaches typically decouple node representation learning from the ranking objective and depend heavily on the topological structure of target networks, leading to feature-task inconsistency and poor cross-network generalization. This paper proposes a novel framework that leverages causal representation learning to obtain robust and invariant node embeddings for cross-network ranking tasks. Specifically, we introduce an influence-aware causal node embedding module within an autoencoder architecture to extract node embeddings that are causally related to node importance. Furthermore, we design a unified optimization framework incorporating a causal ranking loss that jointly optimizes reconstruction and ranking objectives, thereby enabling mutual reinforcement between node representation learning and ranking optimization. This design allows the proposed model to be trained on synthetic networks and to generalize effectively across diverse real-world networks. Extensive experiments on multiple benchmark datasets demonstrate that the proposed model consistently outperforms state-of-the-art baselines in terms of both ranking accuracy and cross-network transferability, offering new insights for network analysis and engineering applications-particularly in scenarios where the target network's structure is inaccessible in advance due to privacy or security constraints.

翻译：理解和量化节点重要性是网络科学与工程中的一个基本问题，支撑着影响力最大化、社交推荐和网络拆解等广泛的应用。先前的研究通常依赖于中心性度量或利用结构信息的先进图嵌入技术，随后通过下游分类或回归任务来识别关键节点。然而，这些方法通常将节点表示学习与排序目标解耦，并且严重依赖目标网络的拓扑结构，导致特征-任务不一致以及跨网络泛化能力差。本文提出了一种新颖的框架，该框架利用因果表示学习来获得用于跨网络排序任务的鲁棒且不变的节点嵌入。具体而言，我们在自编码器架构中引入了一个影响感知因果节点嵌入模块，以提取与节点重要性存在因果关系的节点嵌入。此外，我们设计了一个统一的优化框架，该框架结合了因果排序损失，以联合优化重构目标和排序目标，从而实现节点表示学习与排序优化之间的相互促进。这种设计使得所提出的模型能够在合成网络上进行训练，并能有效地泛化到多样化的现实世界网络中。在多个基准数据集上进行的大量实验表明，所提出的模型在排序准确性和跨网络可迁移性方面均持续优于最先进的基线方法，为网络分析和工程应用提供了新的见解——特别是在由于隐私或安全约束而无法预先获取目标网络结构的场景中。