<p>Graph (or network) is a mathematical structure that has been widely used to model relational data. As real-world systems get more complex, multilayer (or multiple) networks are employed to represent diverse patterns of relationships among the objects in the systems. One active research problem in multilayer networks analysis is to study the common properties of the networks. In this paper, we study whether multilayer networks share the same degree-correction parameters, which is a special case of the widely studied common invariant subspace problem. We first attempt to answer this question by means of hypothesis testing. The null hypothesis states that the multilayer networks share the same degree-correction parameters, and under the alternative hypothesis, there exist at least two networks that have different degree-correction parameters. We propose a weighted degree difference test, derive the limiting distribution of the test statistic and provide an analytical analysis of the power. Simulation study shows that the proposed test has satisfactory performance, and a real data application is provided.</p>