Detecting statistical interactions between input features is a crucial and challenging task. Recent advances demonstrate that it is possible to extract learned interactions from trained neural networks. It has also been observed that, in neural networks, any interacting features must follow a strongly weighted connection to common hidden units. Motivated by the observation, in this paper, we propose to investigate the interaction detection problem from a novel topological perspective by analyzing the connectivity in neural networks. Specially, we propose a new measure for quantifying interaction strength, based upon the well-received theory of persistent homology. Based on this measure, a Persistence Interaction Dection (PID) algorithm is developed to efficiently detect interactions. Our proposed algorithm is evaluated across a number of interaction detection tasks on several synthetic and real-world datasets with different hyperparameters. Experimental results validate that the PID algorithm outperforms the state-of-the-art baselines.