This contribution discusses methods for reconstructing the links of past physical networks, based on archaeological site locations and mathematical models of few parameters. Networks are ubiquitous features of human culture. They structure the geographical patterning of the archaeological record strongly. But while material evidence of networked social interaction is abundant (e.g. similarities in artefact types and technologies), preserved physical remains of the networks (such as roads) are much rarer, making it difficult, if not impossible, to understand the spatial structure of cultural exchange and diffusion. This raises the intractably complex problem of optimal physical network reconstruction, based solely on the known locations of archaeological finds or sites. We address the tractable subproblem of plausible reconstruction of network links. Using a small sample set of Late Bronze Age settlement sites in and around the Mediterranean, we explore model-based network reconstruction from sparse and legacy archaeological data. A hierarchical model is provided by a network-adapted version of Renfrew and Level’s (1979) classic XTENT formula. We show that a GIS-based implementation, that utilises cost surfaces, offers significantly increased realism and analytical advantages. Our approach represents an alternative (with its specific strengths and weaknesses) to more data-intense and computationally complex approaches, such as agent-based models and simulations. The network reconstruction software used in this study (v.net.models) is available under an open source license.