Clustering method based on the elastic energy functional of directed signed weighted graphs

Abstract This article proposes a new method of clustering based on minimizing the elastic energy functional (EEF) of directed weighted signed graphs. The new method has three distinctive features: the weights on the edges of the graph are set by the original model of the system (fuzzy cognitive map), and each weight represents a causal relationship between the graph vertices (system factors); a clearly formalized criterion for division into clusters; and the order of the vertices generated by the algorithm reflects the ratio of intra-cluster and extra-cluster energy. The proposed functional of the elastic energy reflects the nature of the factor relationship in a socio-economic system. Minimization of the functional is monotonic and does not require user intervention. The algorithm is computationally efficient.