We introduce the concept of a trust network - a decentralized payment infrastructure in which payments are routed as IOUs between trusted entities. The trust network has directed links between pairs of agents, with capacities that are related to the credit an agent is willing to extend another; payments may be routed between any two agents that are connected by a path in the network. The network structure introduces group budget constraints on the payments from a subset of agents to another on the trust network: this generalizes the notion of individually budget constrained bidders. We consider a multi-unit auction of identical items among bidders with unit demand, when the auctioneer and bidders are all nodes on a trust network. We define a generalized notion of social welfare for such budget-constrained bidders, and show that the winner determination problem under this notion of social welfare is NP-hard; however the flow structure in a trust network can be exploited to approximate the solution with a factor of 1 - 1/e. We then present a pricing scheme that leads to an incentive compatible, individually rational mechanism with feasible payments that respect the trust network's payment constraints and that maximizes the modified social welfare to within a factor 1 - 1/e.