Receivable financing is the process whereby cash is advanced to firms against receivables their customers have yet to pay: a receivable can be sold to a funder, which immediately gives the firm cash in return for a small percentage of the receivable amount as a fee. Receivable financing has been traditionally handled in a centralized way, where every request is processed by the funder individually and independently of one another. In this work we propose a novel, network-based approach to receivable financing, which enables customers of the same funder to autonomously pay each other as much as possible, and gives benefits to both the funder (reduced cash anticipation and exposure risk) and its customers (smaller fees and lightweight service establishment). Our main contributions consist in providing a principled formulation of the network-based receivable-settlement strategy, and showing how to achieve all algorithmic challenges posed by the design of this strategy. We formulate network-based receivable financing as a novel combinatorial-optimization problem on a multigraph of receivables. We show that the problem is NP-hard, and devise an exact branch-and-bound algorithm, as well as algorithms to efficiently find effective approximate solutions. Our more efficient algorithms are based on cycle enumeration and selection, and exploit a theoretical characterization in terms of a knapsack problem, as well as a refining strategy that properly adds paths between cycles. We also investigate the real-world issue of avoiding temporary violations of the problem constraints, and design methods for handling it. An extensive experimental evaluation is performed on real receivable data. Results attest the good performance of our methods.