Identifying network dynamics is a critical yet challenging task to to understand the mechanism of real-world social systems. There are two types of algorithms, and one requires the knowledge of self-dynamics function, interactive function, and interactive network to sparsely identify the network dynamics. Another one does not require any knowledge, but use simple functions to universally approximate complex functions. However, this type of algorithms lack interpretability, and the functional space is too extensive to search efficiently. Thus, to address this issue, this work proposes an Alternating Sparse Identification of Network Dynamics (ASIND) algorithm to sparsely identify the self-dynamics function, interactive function and interactive network alternatively. Extensive experiments are conducted to show the state-of-the-art identification and 100-steps prediction performance compared to the baseline. The experimental results also show the weak identifiability of interactive network, that means different networks can generate highly similar trajectories of network dynamics. The code is available at https://github.com/KMY-SEU/ASIND.