Message passing and cyclicity transition

Fuente: arXiv
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Main Author: Hiraoka, Takayuki
Format: Preprint
Published: 2026
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author Hiraoka, Takayuki
author_facet Hiraoka, Takayuki
contents Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation remains elusive. We show that the message passing solutions commonly associated with the probability of belonging to the giant component actually identify reachability from cycles. This interpretation generally applies to bond and site percolation on any directed or undirected networks. Our findings highlight the distinction between transition in cyclicity and the emergence of the giant component.
format Preprint
id arxiv_https___arxiv_org_abs_2604_01201
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Message passing and cyclicity transition
Hiraoka, Takayuki
Physics and Society
Statistical Mechanics
Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation remains elusive. We show that the message passing solutions commonly associated with the probability of belonging to the giant component actually identify reachability from cycles. This interpretation generally applies to bond and site percolation on any directed or undirected networks. Our findings highlight the distinction between transition in cyclicity and the emergence of the giant component.
title Message passing and cyclicity transition
topic Physics and Society
Statistical Mechanics
url https://arxiv.org/abs/2604.01201