# Conditionally Poissonian random digraphs

## TL;DR

This paper introduces a new Poissonian model for directed random graphs, extending previous undirected models, and analyzes its degree distribution and component structure with implications for infection process theory.

## Contribution

It defines a novel directed Poissonian random graph model and characterizes its degree distribution and component structure, connecting to infection process applications.

## Key findings

- Derived the limiting degree distribution of a typical vertex.
- Analyzed the component structure in special cases.
- Established relations to the Norros-Reittu model.

## Abstract

In this short note we define a Poissonian model of directed random graphs which generalises the undirected Poissonian random graph process introduced in [Norros, I.; Reittu, H. "On a conditionally Poissonian graph process." Adv. in Appl. Probab. 38 (2006), no. 1, 59--75]. We discuss the relation of our model to the Norros-Reittu model, characterise the limiting distribution of the degree of a typical vertex and discuss the component structure of the model in some special cases which are relevant to the theory of infection processes.