Analysis of Poisson Networks and Their Relation with Random Cellular Structures

TL;DR

This paper investigates the statistical properties of Poisson networks and reveals that their metric and topological features cannot be accurately modeled by simple Poisson point-based networks, challenging existing assumptions.

Contribution

It provides a detailed analysis showing that common laws like Lewis and Aboav-Wieare are not obeyed in Poisson networks, highlighting limitations of simple models.

Findings

Lewis law is not obeyed in Poisson networks

Aboav-Wieare law is not obeyed in Poisson networks

Metric and topological properties differ from simple models

Abstract

We perform a detailed analysis of the statistical properties of Poisson networks and show that the metric and topological properties of random cellular structures, can not be derived from simple models of random networks based on a poisson point distribution [1]. In particular we show that Lewis and Aboav-Wieare laws are not obeyed in these network.