In the current study, we used topological data analysis of fMRI data for exploring neurophysiological mechanisms underlying the execution of deceptive actions. We used the results of the analysis of psychophysiological interactions (PPI) of fMRI data, obtained during an earlier experiment where subjects were required to mislead an opponent through sequential execution of deceptive and honest claims. A connectivity matrix based on PPI analysis was processed with the methods of algebraic topology. With this approach, we confirmed our previous findings that the increase in local activity and psychophysiological interactions of the left caudate nucleus is associated with the execution of deceptive actions. It is also in line with our hypothesis that involvement of the left caudate nucleus in brain processing of deception reflects the process of activation of error detection mechanism. In contrast to this finding, the right caudate nucleus was most frequently observed in the selected cliques associated with honest actions in comparison with deceptive ones. This observation points to possible differential role of left and right caudate nuclei in processing deceptive and honest actions, so it can be further investigated in future research. Topological analysis of higher-order organization of functional interactions revealed three cycles encompassing different sets of brain regions. Those regions are associated with executive control, error detection and sociocognitive processes, involvement of which in deception execution was hypothesized in previous studies. The fact of observation of such loops of functionally integrated brain regions demonstrates the possibility of parallel functioning of above-mentioned mechanisms and substantially extends the current view on neurobiological basics of deceptive behavior.