Circulation is the characteristic feature of successful currency systems, from community currencies to cryptocurrencies to national currencies. This talk will present a network approach to studying the circulation of money within such systems, touching on the data, the theory, and the tools. Modern payment infrastructure keeps digital transaction records that capture an ever greater share of circulation. A theory of walk processes on networks gives us a solid basis for representing such data, and lets us develop highly effective network analysis tools. We will discuss applied analyses of Sarafu, a digital community currency active in Kenya, and of a mobile money system elsewhere in Africa operating in the national currency. Several specific findings have concrete implications for humanitarian and development policy. More broadly, the ability to study the circulation of digital money in detail stands to accelerate our understanding of payment systems, the currency systems they comprise, the financial systems they underpin, and the economic systems they enable.