the 'small world phenomenon' as observed by the psychologist stanley milgram in the 1960s is that most pairs of people are connected by a short chain of acquaintances. more generally we say a graph exhibits the small world phenomenon if the average distance between vertices is small due to a few random-like edges combined with a highly regular local structure. randomly generated graphs with a power law degree distribution are often used to model large real-world networks. while these graphs have small average distance, they do not have the local structure associated with the small world phenomenon. we define a hybrid model which combines a global graph (a random power law graph) with a local graph (a graph with high local connectivity defined by network flow). we also present an efficient algorithm to extract a highly connected local graph from a given realistic network. we show that the hybrid model is robust in the following sense. given a graph generated by the hybrid model, we can recover a good approximation to the original local graph in polynomial time.