The literature on knowledge transfer has long recognized the importance of social relations as a conduit of knowledge transfer. Two distinct features of social relations have been examined extensively: their strength and structure. Their effects on knowledge transfer remain unclear, however, and researchers have attended to one or the other of two constraints — information loss and transfer cost — in efforts to elucidate them. Yet, few studies analyse the joint effects of these constraints on knowledge transfer in a network directly. To examine their interaction, this article develops an agent-based simulation and experiment with four different kinds of relations: a sparse network with weak ties, a sparse network with strong ties, a dense network with weak ties and a dense network with strong ties. At the individual level, the study finds that dense networks comprised of weak ties afford more valuable knowledge if information loss is trivial and the cost of initiating ties is larger than the cost of transfer, but that the value of density declines rapidly as information loss increases. At the organizational level, in contrast, sparse networks with strong ties appear optimal for knowledge transfer via social relations.