Random multi-hooking networks

TL;DR

This paper introduces a new class of multi-hooking networks where multiple copies of a seed are randomly attached at each step, analyzing their degree profiles and distances to understand their structural properties.

Contribution

The paper defines and analyzes the properties of multi-hooking networks, including degree evolution and distance metrics, providing insights into their structural behavior.

Findings

Local average degree experiences phases over time

Global average degree remains invariant to building sequence

Expected number of nodes with smallest degree analyzed

Abstract

We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees -- the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.