This study examines the hypothesis that the phenomenon of consciousness is linked to the formation of complex signal cycles within a network of neuronal cells. To test this hypothesis, a graph-theoretic formalism is employed within a mathematical modeling framework, where neurons and/or their clusters serve as vertices and synaptic connections as edges. Graphs representing the brain’s connectome are constructed, and EEG data are analyzed. A specialized algorithm is used to analyze signals within the complex network, enabling a search for correlations between signal transmission frequencies and EEG frequencies. Algorithmic analysis confirms the thesis that, as a system of neuron-like graphs (characteristic of brain structure, where receptor-effector connections are realized) increases in complexity, a so-called percolation transition — analogous to a physical phase transition — occurs. This process gives rise to cyclic structures, which are associated with the emergence of complex network functions. These structures are identified through the analysis of EEG data. These theoretical concepts are compared with experimental findings from other researchers regarding the significance of giant cycles in the manifestation of consciousness.