Saved in:
Bibliographic Details
Main Authors: Wang, Zeyu, Sergei, Kudria, Chen, Jingbang, Chen, Jiawei, Wang, Xinyu, Luo, Xiaodong, Wang, Can
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.17492
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911692048302080
author Wang, Zeyu
Sergei, Kudria
Chen, Jingbang
Chen, Jiawei
Wang, Xinyu
Luo, Xiaodong
Wang, Can
author_facet Wang, Zeyu
Sergei, Kudria
Chen, Jingbang
Chen, Jiawei
Wang, Xinyu
Luo, Xiaodong
Wang, Can
contents Signed graphs are widely used to analyze complex systems such as social, political, and biological networks. The notion of balance, a key concept of signed graphs, reflects the stability of relationships. While it has been extensively studied in deterministic graphs, real-world networks often exhibit uncertainty in their connections, which traditional approaches struggle to address. To bridge this gap, we introduce the concept of balance rate, a metric for quantifying the degree of balance in uncertain signed graphs, and prove that computing it exactly is NP-hard, motivating the need for efficient estimation methods. We propose a novel Rao-Blackwellized spanning-tree estimator that achieves near-linear time complexity per sample by leveraging graph decomposition and structural properties. We also construct asymptotically justified confidence intervals using the Delta method. Experiments on real-world datasets demonstrate the efficiency and effectiveness of our approach, enabling scalable balance analysis in uncertain signed graphs.
format Preprint
id arxiv_https___arxiv_org_abs_2605_17492
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Finding the Balance Rate of Uncertain Signed Graphs
Wang, Zeyu
Sergei, Kudria
Chen, Jingbang
Chen, Jiawei
Wang, Xinyu
Luo, Xiaodong
Wang, Can
Data Structures and Algorithms
Signed graphs are widely used to analyze complex systems such as social, political, and biological networks. The notion of balance, a key concept of signed graphs, reflects the stability of relationships. While it has been extensively studied in deterministic graphs, real-world networks often exhibit uncertainty in their connections, which traditional approaches struggle to address. To bridge this gap, we introduce the concept of balance rate, a metric for quantifying the degree of balance in uncertain signed graphs, and prove that computing it exactly is NP-hard, motivating the need for efficient estimation methods. We propose a novel Rao-Blackwellized spanning-tree estimator that achieves near-linear time complexity per sample by leveraging graph decomposition and structural properties. We also construct asymptotically justified confidence intervals using the Delta method. Experiments on real-world datasets demonstrate the efficiency and effectiveness of our approach, enabling scalable balance analysis in uncertain signed graphs.
title Finding the Balance Rate of Uncertain Signed Graphs
topic Data Structures and Algorithms
url https://arxiv.org/abs/2605.17492