Structure matters: Assessing the statistical significance of network topologies.

Network analysis has found widespread utility in many research areas. However, assessing the statistical significance of observed relationships within networks remains a complex challenge. Traditional node permutation tests are often insufficient in capturing the effect of changing network topology by creating reliable null distributions. We propose two randomization alternatives to address this gap: random rewiring and controlled rewiring. These methods incorporate changes in the network topology through edge swaps. However, controlled rewiring allows for more nuanced alterations of the original network than random rewiring. In this sense, this paper introduces a novel evaluation tool, the Expanded Quadratic Assignment Procedure (EQAP), designed to calculate a specific p-value and interpret statistical tests with enhanced precision. The combination of EQAP and controlled rewiring provides a robust network comparison and statistical analysis framework. The methodology is exemplified through two real-world examples: the analysis of an organizational network structure, illustrated by the Enron-Email dataset, and a social network case, represented by the UK Faculty friendship network. The utility of these statistical tests is underscored by their capacity to safeguard researchers against Type I errors when exploring network metrics dependent on intricate topologies.