  Alliances and conflicts in social, political and economic relations can be
represented by positive and negative edges in signed networks. A cycle is said
to be positive if the product of its edge signs is positive, otherwise it is
negative. Then, a signed network is balanced if and only if all its cycles are
positive. An index characterizing how much a signed network deviates from being
balanced is known as a global balance index. Here we give a step forward in the
characterization of signed networks by defining a local balance index, which
characterizes how much a given vertex of a signed network contributes to its
global balance. We analyze the mathematical foundations and unique structural
properties of this index. Then, we apply this index to the study of the
evolution of international relations in the globe for the period 1816-2014. In
this way we detect and categorize major historic events based on balance
fluctuations, helping our understanding towards new mixed approaches to history
based on network theory.
