This paper, authored by M. S. Wertheim, presents a reformulation of statistical thermodynamics for fluids with highly directional attractive forces. The molecular model consists of a repulsive core and multiple sites of very short-ranged attraction. The authors explore the relationship between graph cancellation in the fugacity expansion and steric incompatibility between repulsive and attractive interactions involving several molecules. They use steric effects to control density parameters in a limited regrouping of bonds, which helps in minimizing the Helmholtz free energy \( A \). The paper derives graphical expressions for \( A \) and the pressure \( p \), and identifies analogs of \( s \)-particle direct correlation functions and the Ornstein-Zernike equation. The approach avoids reducing the model to a single level of description where sites replace molecules as primary units, instead treating each species as a monomeric unit with a specified set of bonded attraction sites. The decision on whether a site is bonded is based on graph theory and the use of Mayer \( f \)-functions, allowing for physically motivated manipulations. The paper provides the mechanics and physical justification for the reformulation, with possible approximation theories discussed in a companion paper.This paper, authored by M. S. Wertheim, presents a reformulation of statistical thermodynamics for fluids with highly directional attractive forces. The molecular model consists of a repulsive core and multiple sites of very short-ranged attraction. The authors explore the relationship between graph cancellation in the fugacity expansion and steric incompatibility between repulsive and attractive interactions involving several molecules. They use steric effects to control density parameters in a limited regrouping of bonds, which helps in minimizing the Helmholtz free energy \( A \). The paper derives graphical expressions for \( A \) and the pressure \( p \), and identifies analogs of \( s \)-particle direct correlation functions and the Ornstein-Zernike equation. The approach avoids reducing the model to a single level of description where sites replace molecules as primary units, instead treating each species as a monomeric unit with a specified set of bonded attraction sites. The decision on whether a site is bonded is based on graph theory and the use of Mayer \( f \)-functions, allowing for physically motivated manipulations. The paper provides the mechanics and physical justification for the reformulation, with possible approximation theories discussed in a companion paper.