Using bootstrap procedures for testing the modular partition inferred via leading eigenvector community detection algorithm

Abstract

Modularity and modular structures can be recognized at various levels of biological organization and in various domains of studies. Recently, algorithms based on network analysis came into focus. And while such a framework is a powerful tool in studying modular structure, those methods usually pose a problem of assessing statistical support for the obtained modular structures. One of the widely applied methods is the leading eigenvector, or Newman's spectral community detection algorithm. We conduct a brief overview of the method, including a comparison with some other community detection algorithms and explore a possible fine-tuning procedure. Finally, we propose an adapted bootstrap-based procedure based on Shimodaira's multiscale bootstrap algorithm to derive approximately unbiased p-values for the module partitions of observations datasets. The proposed procedure also gives a lot of freedom to the researcher in constructing the network construction from the raw numeric data, and can be applied to various types of data and used in diverse problems concerning modular structure. We provide an R language code for all the calculations and the visualization of the obtained results for the researchers interested in using the procedure.