An algebraic interpretation of multigraph networks is introduced in relation to conscious experience, brain and body. These multigraphs have the ability to merge by an associative binary operator \(\odot \), accounting for biological composition. We also study a mathematical formulation of splitting layers, resulting in a formal analysis of the transition from conscious to non-conscious activity. From this construction, we recover core structures for conscious experience, dynamical content and causal constraints that conscious interactions may impose. An important result is the (...) prediction of structural topological changes after conscious interactions. These results may inspire further use of formal mathematics to describe and predict new features of conscious experience while aligning well with formal tries to mathematize phenomenology, phenomenological tradition and applications to artificial consciousness. (shrink)