Walk-based measure of balance in signed networks: Detecting lack of balance in social networks

There is a longstanding belief that in social networks with simultaneous friendly and hostile interactions (signed networks) there is a general tendency to a global balance. Balance represents a state of the network with a lack of contentious situations. Here we introduce a method to quantify the degree of balance of any signed (social) network. It accounts for the contribution of all signed cycles in the network and gives, in agreement with empirical evidence, more weight to the shorter cycles than to the longer ones. We found that, contrary to what is generally believed, many signed social networks, in particular very large directed online social networks, are in general very poorly balanced. We also show that unbalanced states can be changed by tuning the weights of the social interactions among the agents in the network.