The resulting effect of global international relations is an intricate and dynamic web of alliances and conflicts. Here, we represent this web as a time-evolving signed network and define an index quantifying the proximity of every nation to its balanced condition. This condition emerges when a given nation belongs to a bloc of allies that only have enmities with a different confronted bloc. However, we find that large blocs of allies percolated by a tiny clique of mutual enemies, which are ubiquitous across history, are very unstable in terms of their balanced condition. We design a quantitative history approach to identify the nations playing a fundamental role in major events in human history over a period of almost 200 years. It is combined with historic narrative and the sociopolitical theory of “balance of power” to build up a new mixed approach to history based on network theory.