# Randomizing growing networks with a time-respecting null model

## TL;DR

This paper introduces a null model for growing networks that preserves temporal and degree information, enabling more accurate significance testing of network properties.

## Contribution

The paper presents a novel time-respecting null model for growing networks that maintains temporal linking patterns and degree sequences, improving analysis accuracy.

## Key findings

- Citation networks show different degree correlations under the model.
- Degree and PageRank metrics are affected by temporal patterns.
- The model can be used to assess significance of structural properties.

## Abstract

Complex networks are often used to represent systems that are not static but grow with time: people make new friendships, new papers are published and refer to the existing ones, and so forth. To assess the statistical significance of measurements made on such networks, we propose a randomization methodology---a time-respecting null model---that preserves both the network's degree sequence and the time evolution of individual nodes' degree values. By preserving the temporal linking patterns of the analyzed system, the proposed model is able to factor out the effect of the system's temporal patterns on its structure. We apply the model to the citation network of Physical Review scholarly papers and the citation network of US movies. The model reveals that the two datasets are strikingly different with respect to their degree-degree correlations, and we discuss the important implications of this finding on the information provided by paradigmatic node centrality metrics such as indegree and Google's PageRank. The randomization methodology proposed here can be used to assess the significance of any structural property in growing networks, which could bring new insights into the problems where null models play a critical role, such as the detection of communities and network motifs.