The paper contributes to the theory of structural balance in signed social networks. We extend two known measures of partial balance onto more general class of the so called weighted networks where the edges weights represent the strength of the links. In addition, we introduce new measure of partial balance which takes into account a possible way how one can balance original unbalanced network with minimal “costs”.

Using these results, we formalize and study weighted network models of the interaction between main religious movements (Pharisees, Sadducees, Essenes/resp. Qumranites) and Hasmonean rulers in Judea for several consequent periods in II-I centuries BCE. We make an attempt to reconstruct the system of relations in these networks with four vertices and evaluate the degrees of partial balance for each weighted network.

Finally, we compare calculated characteristics of the network models with some historical facts dating back to ancient manuscripts and archaeological findings. It turns out that the considered measures of partial balance of these weighted network models are in good agreement with known historical facts in Judea at least for the chosen historical periods.