The Watts-Strogatz model describes a mechanism of generating small-world networks.
The idea is to start from a ring network in which each node is connected a fixed number of its closest neighbors. After that, a rewiring is performed in which each link present in the network has a probability $p$ of changing one of its endpoints to a new random node. The closer $p$ to 1, the more random is the network.
Is there a similar small-world model for bipartite graphs? That is, is there a mechanism for generating random bipartite graphs that possess the usual properties of small-world networks (a.k.a., the maximum of the minimum distance between any pair of nodes scales no higher than as the logarithm of the number of nodes)?