# Algebraic algorithms for even circuits in graphs

## TL;DR

This paper introduces an algebraic algorithm to identify and enumerate indecomposable even circuits in graphs, with applications to directed cycles in digraphs, advancing graph analysis techniques.

## Contribution

The paper presents a novel algebraic approach for detecting and listing indecomposable even circuits, extending its application to directed cycle analysis in digraphs.

## Key findings

- Efficient algebraic algorithm for even circuit detection
- Method to list all indecomposable even circuits
- Application to directed cycle analysis in digraphs

## Abstract

We present an algebraic algorithm to detect the existence of and to list all indecomposable even circuits in a given graph. We also discuss an application of our work to the study of directed cycles in digraphs.