# Random graphs and their subgraphs

## TL;DR

This paper investigates properties of random graphs and their subgraphs, analyzing how features like connectedness and degree distributions are inherited, and provides formulas and connections relevant to network modeling.

## Contribution

It introduces formulas for degree variance in preferential attachment models and links weighted graphs to electrical networks, enhancing understanding of network properties.

## Key findings

- Degree variance formula for preferential attachment models
- Inheritance of connectedness and degree distributions in subgraphs
- Connection between weighted graphs and electrical networks

## Abstract

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are inherited by differently constructed subgraphs. We also give a formula for the variance of the degrees of fixed nodes in the preferential attachment model and additionally draw a connection between weighted graphs and electrical networks.