In the past two decades, there has been a notable surge in network data. This proliferation has spurred significant advancements in methods for analyzing networks across various disciplines, including computer science, information sciences, biology, bioinformatics, physics, economics, sociology, and health science. Graph two-sample hypothesis testing, aimed at discerning differences between two populations of networks, arises naturally in diverse scenarios. In this paper, we delve into the essential yet intricate task of testing for equivalence between two networks. There are many testing procedures available. For instance, the t-test based on subgraph counts is one of the methods. In this paper, we propose a new test method by using the empirical likelihood. We run extensive simulations to evaluate the performance of the proposed method and apply it a real-world network. Based on the simulation experiments and real data application, the empirical likelihood test consistently outperforms existing subgraph count tests.