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To understand the mechanisms of formation of such signed networks, social balance theory sheds light on the dynamics of positive and negative connections. In particular, it characterizes the proverbs \u2018a friend of my friend is my friend\u2019 and \u2018an enemy of my enemy is my friend\u2019. In this work, we propose a nonparametric inference approach to assessing empirical evidence for balance theory in real-world signed networks. We first characterize the generating process of signed networks with node exchangeability and propose a nonparametric sparse signed graphon model. Under this model, we construct confidence intervals for the population parameters associated with balance theory and establish their theoretical validity. Our inference procedure is as computationally efficient as a simple normal approximation, but yields higher-order accuracy. By applying our method, we find strong real-world evidence for balance theory in signed networks across various domains, extending its applicability beyond social psychology.<\/jats:p>","DOI":"10.1093\/biomet\/asag031","type":"journal-article","created":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:32:03Z","timestamp":1776771123000},"source":"Crossref","is-referenced-by-count":0,"title":["Nonparametric inference for balance in signed networks"],"prefix":"10.1093","volume":"113","author":[{"given":"Xuyang","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Computational Science, University of Pennsylvania , 209 S. 33rd Street , Philadelphia, Pennsylvania 19104, U.S.A. xuyangc@sas.upenn.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yinjie","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Chicago , 5734 S. University Avenue , Chicago, Illinois 60637, U.S.A. yinjie@uchicago.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3543-9924","authenticated-orcid":false,"given":"Weijing","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Carnegie Mellon University , 5000 Forbes Avenue , Pittsburgh, Pennsylvania 15213, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,4,28]]},"reference":[{"key":"2026080400215246600_asag031-B1","first-page":"1981","article-title":"Mixed membership stochastic blockmodels","volume":"9","author":"Airoldi","year":"2008","journal-title":"J. Mach. Learn. 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