# Fitting the Linear Preferential Attachment Model

## TL;DR

This paper develops methods to fit a 5-parameter linear preferential attachment model to network data, providing estimators that are consistent and effective in both full history and snapshot scenarios, with applications to real data.

## Contribution

It introduces novel estimation techniques for the linear preferential attachment model applicable to different data availability scenarios, including maximum likelihood and combined method of moments approaches.

## Key findings

- MLE estimator is strongly consistent and asymptotically normal.
- Proposed estimator performs well compared to MLE in snapshot data.
- Methods are validated through simulations and real data examples.

## Abstract

Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network data under two data scenarios. In the case where full history of the network formation is given, we derive the maximum likelihood estimator of the parameters and show that it is strongly consistent and asymptotically normal. In the case where only a single-time snapshot of the network is available, we propose an estimation method which combines method of moments with an approximation to the likelihood. The resulting estimator is also strongly consistent and performs quite well compared to the MLE estimator. We illustrate both estimation procedures through simulated data, and explore the usage of this model in a real data example.