Dyadic imbalance in networks

Abstract

Abstract The study of balance in signed networks has been a key topic for over 80 years. Starting with Heider’s theory of structural balance and Harary’s balance theorem, the measurement and understanding of structural balance in networks has grown exponentially. Most theoretical and empirical studies, however, focus on balance on the network as a whole, even though the degree of balance may strongly vary within the network. Our study makes two key contributions to this literature. First, we offer a methodology for measuring balance between nodes in a network. We show that dyadic (im)balance reveals significant information about localized balance that is not apparent in a global metric of balance. Second, we show that this metric can be applied to data containing multiple relations, for example, friendship, enmity, trade and fights, which reveals balance and imbalance otherwise hidden when focusing on only two relations (e.g. friends and enemies). Namely, while balance typically involves unweighted signed networks, multiple relations can naturally be condensed into a weighted signed network where positive (negative) weights correspond to a sum of positive (negative) relations between nodes. Our dyadic imbalance metric can then be applied to this and any other weighted signed network. These findings are illustrated with an international relations network as well as a network on roll call votes in the US Senate and compared to a null model that preserves network structure. We find weak agreement with Heider’s balance theory, including imbalance that decreases in time, and imbalance that is generally lower than our null model.