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A remarkable phenomenon in the time evolution of many networks such ascultural, political, national and economic systems, is the recurrent transitionbetween the states of union and division of nodes. In this work, we propose aphenomenological modeling, inspired by the maxim "long union divides and longdivision unites", in order to investigate the evolutionary characters of thesenetworks composed of the entities whose behaviors are dominated by these twoevents. The nodes are endowed with quantities such as identity, ingredient,richness (power), openness (connections), age, distance, interaction etc. whichdetermine collectively the evolution in a probabilistic way. Depending on atunable parameter, the time evolution of this model is mainly an alternativedomination of union or division state, with a possible state of final uniondominated by one single node.

Long division unites - long union divides, a model for social network evolution