Silence as a Social Equilibrium: A Graph-Domination Model of Recognition Asymmetry

This paper reconceptualizes silence not as an individual pathology or commu- nication breakdown but as a rationally emergent social equilibrium. Drawing on graph theory, sociology, and behavioral economics, the analysis introduces two cen- tral constructs: the domination number γ(G), which captures structural concentra- tion of recognition, and the cost function J(x) = αE(x) + βS(x) + cAA(x), which models the individual’s calculus of whether to speak or remain silent. Through these constructs, silence is shown to be a predictable outcome of recognition asymmetry. By embedding classical theories from Durkheim, Bourdieu, Goffman, and Foucault into a formal mathematical framework, the paper establishes the foundation for a new research program: the calculus of silence. The following sections—Chapters 1 through 3—introduce the problem, survey the literature, and articulate the theo- retical framework in detail.