Hierarchy depth in directed networks

TL;DR

This paper introduces two measures of hierarchy depth in directed networks, analyzes their differences, and examines their behavior in random graphs of various sizes and densities.

Contribution

It defines rooted and relative depth measures for flow hierarchy and compares their properties and behaviors in different network models.

Findings

Rooted and relative depth measures differ in their behavior.

Depth measures vary with network size and density.

Results help understand hierarchy structures in directed networks.

Abstract

We explore depth measures for flow hierarchy in directed networks. We define two measures -- rooted depth and relative depth, and discuss differences between them. We investigate how the two measures behave in random Erdos-Renyi graphs of different sizes and densities and explain obtained results.