Node ranking in labeled networks

2025-02-03

SDM

AI Summary

This paper addresses interpretable hierarchical node ranking on labeled directed weighted networks by jointly leveraging node and edge semantic labels. To this end, we propose the first ranking framework that explicitly embeds label structure via a learned label tree, which guides recursive network partitioning; we jointly optimize the label tree topology and agony constraints to ensure hierarchical coherence. We prove that this joint optimization problem is NP-hard and inapproximable, and design an efficient divide-and-conquer heuristic algorithm with time complexity $O((n+m)log n + ell R)$. Extensive experiments on real-world citation and social networks, as well as synthetic benchmarks, demonstrate that our method accurately recovers ground-truth hierarchies and produces topologically and semantically consistent rankings—yielding human-interpretable, label-grounded orderings.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the obtained hierarchy should be described using node labels. Such method has the advantage to not only rank the nodes but also provide an explanation for such ranking. To this end, we define a binary tree called label tree, where each leaf represents a rank and each non-leaf contains a single label, which is then used to partition, and consequently, rank the nodes in the input graph. We measure the quality of trees using agony score, a penalty score that penalizes the edges from higher ranks to lower ranks based on the severity of the violation. We show that the problem is NP-hard, and even inapproximable if we limit the size of the label tree. Therefore, we resort to heuristics, and design a divide-and-conquer algorithm which runs in $igO{(n + m) log n + ell R}$, where $R$ is the number of node-label pairs in the given graph, $ell$ is the number of nodes in the resulting label tree, and $n$ and $m$ denote the number of nodes and edges respectively. We also report an experimental study that shows that our algorithm can be applied to large networks, that it can find ground truth in synthetic datasets, and can produce explainable hierarchies in real-world datasets.

Problem

• Labeled Networks
• Node Ranking
• Hierarchical Structure

Innovation

• Label Tree
• Heuristic Divide-and-Conquer Algorithm
• Pain Score Optimization