# Massey products for graph homology

## TL;DR

This paper demonstrates the Koszul property of the operad for modular operads and uses it to develop higher operations on graph homology, revealing its rational homotopy type.

## Contribution

It establishes the Koszulness of the modular operad operad and constructs higher composition operations on graph homology for the first time.

## Key findings

- Operad encoding modular operads is Koszul.
- Constructed higher composition operations on graph homology.
- Characterized the rational homotopy type of graph homology.

## Abstract

This paper shows that the operad encoding modular operads is Koszul. Using this result we construct higher composition operations on (hairy) graph homology which characterize its rational homotopy type.