Further Algebraic Results in the Theory of Balance

In an article published in 1970 in the French journal Mathématiques et Sciences Humaines , Flament described a number of mathematical results pertaining to an algebraic formulation of the theory of balance in signed graphs. This paper describes some additional results based on those discussed by Flament. These newer results are especially useful for the development of algorithms for calculating the line index of balance in the study of specific networks arising in psychological and sociological research.