Inferring tie strengths (strong vs. weak) is a core task in network analysis, often guided by the Strong Triadic Closure (STC) principle. In multilayer networks, such as social platforms or biological systems, applying STC independently to each layer can lead to inconsistent tie labels, undermining interpretations that rely on coherent relationship semantics across layers. We propose new formulations, multilayer STC and its extension STC+, which are axiomatically grounded and enforce cross-layer consistency. These problems are NP-hard; we present efficient 2- and 6-approximation algorithms alongside exact solutions. Experiments on real-world networks demonstrate that our methods produce consistent tie strength labelings with a transparent structural justification, significantly improving over the baselines.

翻译：在网络分析中，推断边强度（强/弱）是一项核心任务，通常遵循强三元闭包原则。在多层级网络（如社交平台或生物系统）中，独立对每一层应用强三元闭包可能导致边标签不一致，从而破坏依赖于跨层关系语义一致性的解释。我们提出新的形式化框架——多层强三元闭包及其扩展STC+，它们具有公理化基础并强制实现跨层一致性。这些问题属于NP难问题；我们提出了高效的2-近似和6-近似算法，同时提供精确解法。在真实网络上的实验表明，我们的方法能生成具有透明结构解释的致密边强度标注，显著优于基线方法。