A random (or pseudorandom) graph is a graph in which properties such as the number of graph vertices and graph edges are determined in some random way. Random graph models are generated to analyze and model component sizes, degree distributions, power laws, and so on. This Demonstration shows five types of random graphs to be used as optional distributions to the command RandomGraph introduced in Mathematica 8. You can also vary the values of their specific parameters. The coloring of the vertices is also random.