Scientific publications

М.А. Булгакова, Д.В. Кузютин, Н.В. Смирнова, И.Р. Тантлевский.

Характеристическая функция в сетевой модели взаимовлияния религиозно-идеологических течений

// Математическая Теория Игр и ее Приложения, т. 18, в. 2. 2026. C. 3-22

Mariia A. Bulgakova, Denis V. Kuzyutin, Nadezhda V. Smirnova, Igor R. Tantlevski. Characteristic function for network model of the interaction between religious movements // Mathematical game theory and applications. Vol 18. No 2. 2026. Pp. 3-22

Keywords: networks, signed graphs, structural balance, weighted network, cooperative game, characteristic function, convex game, the Shapley value, pairwise stability

This article contributes to the theory of structural balance in signed networks. For a class of so-called weighted networks, where edge weights reflect the strength of links, we introduce a characteristic function (CF) based on the weights of balanced cycles. A convexity theorem for this CF is proved for a complete network with finite set of vertices. Using the introduced CF, we provide quantitative estimates of players’ power based on the distribution of weights on the network edges. The well-known property of pairwise stability for networks is extended to this class of weighted networks. The results are demonstrated using network models of the relationships between religious movements and authority in Judea (2nd-1st centuries BCE), based on known historical evidence.

Indexed at RSCI, RSCI (WS)

Last modified: July 15, 2026