On generating random network structures: Connected graphs

In this paper we present the set of base algorithms for generating connected random graphs (RG). RG can be used for testing different algorithms on networks. The fast algorithms with proved properties are presented for random generation of connected graphs, sugraphs (subgraphs on the complete set of nodes) and others in conditions of given restrictions, such as limited node degree, given node degrees, different probabilities of edges existence etc. Special attention is given to generating graphs "similar to real networks." The algorithms are presented in the Pascal-like pseudo code.