It is appealing to disclose the state of an animal as well as the functional connectivity of its neuronal circuit by calculating pairwise and higher-order interactions (HOI) among neuronal activity. Here, we present a systematic approach to achieve these goals by analysing the spiking activity of simultaneously recorded neurons. To this end, we first developed a method to extract significant pairwise and triple-wise interactions among neurons. Using statistically significant data, we then analysed pairwise and HOI from large-scale spiking activities in visual areas of mice during natural movies [1]. Our analysis revealed a general pattern of average positive pairwise and negative triple-wise interactions across all visual areas. To uncover the hidden input motifs underlying these results, we superimposed the obtained interactions onto a recently developed analytical guide map in the plane of triple-wise versus pairwise interactions [2]. This analysis suggested that the motif of excitatory inputs to pairs can explain the observed interactions across visual regions. Furthermore, our results suggested that HOI may distinguish between stationary and running states of the animals. Stationary states exhibited, on average, stronger positive pairwise and negative triple-wise interactions than running states, across all visual regions. The lower average pairwise interaction was a result of a fraction of negative pairwise interactions when the animal was running. Our analysis suggested that this can be a signature of recurrent inhibitory motifs. To further test this hypothesis, we applied our method to another dataset that involved recurrent inhibitory mechanisms [3] and observed similar negative pairwise interactions. Finally, we performed numerical simulations of leaky integrate-and-fire neurons and studied them analytically, which confirmed that the observed negative pairwise interactions can be a result of recurrent inhibitory motifs during running. Our result is consistent with a circuit motif in which top-down feedback during locomotion disinhibits parvalbumin inhibitory neurons, which can then inhibit excitatory neurons through recurrent connections. Our work, therefore, provides a systematic analysis of HOI across visual areas, demonstrating how significant HOI can be measured and used to distinguish neuronal circuits underlying neural dynamics in different behavioural states.