# Bipartitioning of directed and mixed random graphs

## TL;DR

This paper extends the understanding of bipartitioning in random graphs to directed and mixed types, revealing that key properties depend mainly on the total number of directed links, with implications for phase transitions.

## Contribution

It demonstrates that the relation between cluster properties and optimal bipartitions in undirected graphs also applies to directed and mixed graphs, highlighting the role of total directed links.

## Key findings

- Satisfiability threshold aligns with the giant OUT component reaching 1/2.
- Partition cost and cluster properties depend mainly on total directed links.
- Location of replica symmetry breaking transition is primarily influenced by total directed links.

## Abstract

We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the relative size of the giant OUT component reaching~{1/2}. Moreover, when counting undirected links as two directed ones, the partition cost, and cluster properties, as well as location of the replica symmetry breaking transition for these random graphs depend primarily on the total number of directed links and not on their specific distribution.