Long Division Unites or Long Union Divides: a Model for Social Network Evolution

A remarkable phenomenon in the time evolution of many networks such as cultural, political, national and economic systems is the recurrent transition between the states of union and the division of nodes. We propose a phenomenological modeling, inspired by the maxim "long union divides and long division unites" to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events. The nodes are endowed with quantities such as identity, ingredient, richness (power), openness (connections), age, distance, and interaction, which determine collectively the evolution in a probabilistic way. Depending on a tunable parameter, the time evolution of this model is mainly an alternative domination of union or division state, with a possible state of final union dominated by one single node.