Lifetime of links influences the evolution towards structural balance

Abstract A fully connected network is investigated with signed (friendly or hostile) links. We consider a time evolution which drives the network to a structurally balanced state. Usually a hypothesis is made tacitly that the states of links can be permanent. However in real networks these states can fluctuate. In this paper, we assign a lifetime to each link. When a link age exceeds its lifetime, its sign is substituted by a random value ± 1 and its age is set to zero. Then, two asymptotic behaviors are observed. When the lifetime is large, the system is balanced with only small fluctuations. When the lifetime is short, the system fluctuates randomly, far from the balanced state. A crossover is observed between these two regimes. The age distribution of the links depends on the lifetime. The results are discussed in the context of data on selected conflicts between political actors in Europe and the Middle East in the XX century.