In a statistical approach to protein structure analysis, Miyazawa and Jernigan derived a 20×20 matrix of inter-residue contact energies between different types of amino acids. Using the method of eigenvalue decomposition, we find that the Miyazawa-Jernigan matrix can be accurately reconstructed from its first two principal component vectors as Mij=C0＋C1(qi＋qj)＋C2qiqj, with constant C's, and 20q values associated with the 20 amino acids. This regularity is due to hydrophobic interactions and a force of demixing, the latter obeying Hildebrand's solubility theory of simple liquids.