# The Zagreb index of several random models

## TL;DR

This paper analyzes the Zagreb index, a graph-based topological measure, across various random network models, providing mean, variance, and distributional properties for each class.

## Contribution

It introduces new calculations of mean, variance, and asymptotic distributions of the Zagreb index for several classes of random networks.

## Key findings

- Mean and variance of Zagreb index computed for each network class.
- Asymptotic normality established for one class.
- Right-skewed distribution shown for another class.

## Abstract

In this article, we investigate the Zagreb index, a kind of graph-based topological index, of several random networks, including a class of networks extended from random recursive trees, plain-oriented recursive trees, and random caterpillars growing in a preferential attachment manner. We calculate the mean and variance of the Zagreb index for each class. In addition, we prove that the asymptotic distribution of the Zagreb index for the first class is normal, and that the asymptotic distribution of the Zagreb index for the second class is skewed to the right.