Cooperation and competition are two common forms of interpersonal interactions and exploring inter-brain synchronization in these two forms can help to further deliberate the underlying neural mechanisms of interpersonal interactions. Recently, studies revealed that electrode-paired inter-brain synchronization plays an important role in human interactions. This study investigated the neural correlates of interpersonal synchronization at the brain network scale and interaction type. Firstly, the network-wise inter-brain synchronization (NIBS) index reflecting cross-brain network synchronization from the global brain perspective was advanced. Secondly, statistical analysis demonstrated that there are differences in NIBS activities between cooperative and competitive interactions. And a row-filtered depthwise separable convolution network was proposed to classify the NIBS features. Results of EEG hyper-scanning data showed significant differences in NIBS between cooperative and competitive tasks, and a comparative study manifested that the cross-brain synchronization in cooperative tasks is more consistent than that of competitive tasks. The neural decoder using a modified convolution network achieved a peak accuracy of 96.05% under the binary classification(cooperation vs competition).