A signed network is a network with positive and negative signs on the edges. Balance theory [1] explains the forces behind the structure of social systems commonly modeled as static undirected signed networks. A signed graph (network) is balanced if its set of vertices can be partitioned into two subsets such that each negative edge joins vertices belonging to different subsets and each positive edge joins vertices belonging to the same subset [1]. This definition is more often expressed in terms of network triads; which considers triads with an even number of negative edges to be balanced [1]. We expand this modeling to incorporate directionality of the edges, and consider three levels of analysis: micro- (triads), meso- (subgroups), and macro-level (whole network). For micro-level balance, we utilize semicycles of length 3 that satisfy the condition of transitivity and sign consistency. For meso-level balance, we derive measures of cohesiveness (internal solidarity) and divisiveness (external antagonism) to capture balance in subgroups using the most fitting partition of nodes into two groups [2, 3]. For macro-level balance, we use the normalized line index [4, 5], which relies on the proportion of edges whose position suits balance. Figure 1 shows the signed network of 16 tribes in the Papua New Guinea [6] and our proposed approach to evaluating balance at the micro-, meso-, and macro-level. Through extensive computational analysis of 11 social networks, we document frequently repeated patterns of social structure in triads, subgroups, and the whole network across a range of social settings; from college students and Wikipedia users to philosophers and Bitcoin traders.
