Balance and Frustration in Signed Networks under Different Contexts

Frustration index is a key measure for analysing signed networks that has been underused due to its computational complexity. We use an optimisation-based method to analyse frustration as a global structural property of signed networks under different contexts. We provide exact numerical results on social and biological signed networks as well as networks of formal alliances and antagonisms between countries and financial portfolio networks. Molecular graphs of carbon and spin glass models are among other networks that we consider to discuss contextdependent interpretations of the frustration index. The findings unify the applications of a graph-theoretical measure in understanding signed networks. Highlights: Models involving signed networks in 6 different disciplines are analysed An optimisation model is used for a wide range of computational experiments Values of the frustration index in large graphs are computed exactly and efficiently Applications of signed network balance and frustration are unified