This paper models knowledge diffusion as a barter process in which agents exchange different types of knowledge. This is intended to capture the observed practice of informal knowledge trading. Agents are located on a network and are directly connected with a small number of other agents. Agents repeatedly meet those with whom direct connections exist and trade if mutually profitable trades exist. In this way knowledge diffuses throughout the economy. We examine the relationship between network architecture and diffusion performance. We consider the space of structures that fall between, at one extreme, a network in which every agent is connected to n nearest neighbours, and at the other extreme a network with each agent being connected to, on average, n randomly chosen agents. We find that the performance of the system exhibits clear ‘small world’ properties, in that the steady-state level of average knowledge is maximal when the structure is a small world (that is, when most connections are local, but roughly 10 percent of them are long distance). The variance of knowledge levels among agents is maximal in the small world region, whereas the coefficient of variation is minimal. We explain these results as reflecting the dynamics of knowledge transmission as affected by the architecture of connections among agents.