Consistent Tie-Strength Labeling for Multilayer Strong Triadic Closure

TL;DR

This paper introduces multilayer STC and STC+ formulations to ensure consistent tie strength labeling across network layers, with algorithms and experiments demonstrating improved coherence and structural clarity.

Contribution

It proposes axiomatically grounded multilayer STC models and efficient algorithms, addressing inconsistency issues in tie labeling across network layers.

Findings

Algorithms achieve 2- and 6-approximation guarantees.

Methods produce more consistent and interpretable tie labels.

Experiments show significant improvement over baseline methods.

Abstract

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.