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We analyze the 3-parameter family of random networks which are uniform onnetworks with fixed number of edges, triangles, and nodes (between 33 and 66).We find precursors of phase transitions which are known to be present in theasymptotic node regime as the edge and triangle numbers are varied, and focuson one of the discontinuous ones. By use of a natural edge flip dynamics wedetermine nucleation barriers as a random network crosses the transition, inanalogy to the process a material undergoes when frozen or melted, andcharacterize some of the stochastic properties of the network nucleation.

Nucleation during phase transitions in random networks