On generating random network structures: Trees

Random trees (RTs) are widely used for testing various algorithms on tree-type networks and also for generating connected graphs similar to real nets. While random topologies based on RTs are generally accepted as network models, the task of their generation is almost unexplored. In this paper we discuss the set of basic algorithms for generating random trees. The fast algorithms with proven properties are presented for generating random trees under conditions for given restrictions, such as a limited node degree, fixed node degrees, and different probabilities of edge existence. Generating random graphs similar to physical networks are underway.