# Why Do Cascade Sizes Follow a Power-Law?

## TL;DR

This paper provides the first theoretical proof that cascade sizes in a social network model follow a power-law distribution, aligning with empirical observations in large social networks.

## Contribution

It introduces a random directed acyclic graph model and proves that the cascade sizes generated by the CGM follow a power-law distribution, bridging theory and empirical findings.

## Key findings

- Cascade sizes follow a power-law distribution in the model.
- The model's assumptions are consistent with Twitter data.
- Theoretical proof supports empirical observations.

## Abstract

We introduce random directed acyclic graph and use it to model the information diffusion network. Subsequently, we analyze the cascade generation model (CGM) introduced by Leskovec et al. [19]. Until now only empirical studies of this model were done. In this paper, we present the first theoretical proof that the sizes of cascades generated by the CGM follow the power-law distribution, which is consistent with multiple empirical analysis of the large social networks. We compared the assumptions of our model with the Twitter social network and tested the goodness of approximation.