# Scaling in Words on Twitter

## TL;DR

This paper examines how language usage on Twitter scales with city size, revealing superlinear relationships and vocabulary differences, and compares these patterns to traditional text laws like Zipf's and Heaps law.

## Contribution

It provides the first detailed analysis of urban scaling in Twitter language, showing how vocabulary and text properties vary with city population size.

## Key findings

- Twitter volume scales superlinearly with city size.
- Vocabulary usage varies with city size, affecting Zipf's and Heaps law parameters.
- Zipf's law exponent changes with city population.

## Abstract

Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United States. We observe a slightly superlinear urban scaling with the city population for the total volume of the tweets and words created in a city. We then find that a certain core vocabulary follows the scaling relationship of that of the bulk text, but most words are sensitive to city size, exhibiting a super- or a sublinear urban scaling. For both regimes we can offer a plausible explanation based on the meaning of the words. We also show that the parameters for Zipf's law and Heaps law differ on Twitter from that of other texts, and that the exponent of Zipf's law changes with city size.