We propose to test the topological structures of complex networks under the graphon model. Graphon is a nonparametric model for large scale stochastic graphs. Many works have been done on graphon estimation, however it is not easy to interpret the network structures from estimators. We provide an inferential toolkit to study the persistent homology of the graphon landscape which reveals the clustering structure of stochastic networks. Our methods are applied to the neuroscience data related to visual memories.