Abstract: Identifying changes between two networks, also referred to as differential network analysis, has brought new insights to many biological applications. A lot of progress has been made in the development of statistical inference tools for detecting changes between two networks, with most work focused on testing whether two networks are exactly the same, or whether there is an edge that is missing in one network but present in another. However, in many scientific settings, it is often more interesting to identify nodes that have different conditional dependency structures between two networks, which we refer to as differential hub nodes. In this paper, we propose an inferential framework to test whether there is at least one differential hub node in a differential Gaussian graphical model. As a by-product, our proposed test statistic can also be used to test the hypothesis on whether there is a differential edge and construct a confidence interval for the corresponding differential edge. Theoretically, we show that the proposed method yields an asymptotic valid test and that the type II error decreases to zero asymptotically. The proposed method is applied to both simulated data and the Genotype-Tissue Expression (GTEx) data to evaluate whether gene regulatory networks between males and females for different tissues are different.

Key words and phrases: Differential network, Gaussian multiplier bootstrap, hypothesis testing, maximum degree.