Are Social Networks Really Balanced?

There is a long-standing belief that in social networks with simultaneous friendly/hostile interactions (signed networks) there is a general tendency to a global balance. Balance represents a state of the network with 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 evidences, more weight to the shorter than to the longer cycles. We found that, contrary to what is 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.

💡 Research Summary

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The paper revisits the long‑standing assumption that signed social networks tend toward a globally balanced state—a condition in which no “contentious” configurations (e.g., a friend of a friend being an enemy) exist. While classical structural‑balance theory (Heider, Cartwright‑Harary) focuses almost exclusively on triadic (3‑cycle) relationships, real‑world networks contain cycles of many lengths, and the influence of longer cycles on overall balance is not well understood.

To address this gap, the authors introduce a quantitative “balance index” that aggregates the contributions of all signed cycles while weighting shorter cycles more heavily. Formally, a signed adjacency matrix (A) (entries +1 for friendship, –1 for hostility, 0 for no tie) is used. The index is defined as

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