Estimating the abundance or density of populations is fundamental to the conservation and management of species, and as landscapes become more fragmented, maintaining landscape connectivity has become one of the most important challenges for biodiversity conservation. Yet these two issues have never been formally integrated together in a model that simultaneously models abundance while accounting for connectivity of a landscape. We demonstrate an application of using capture-recapture to develop a model of animal density using a least-cost path model for individual encounter probability that accounts for non-Euclidean connectivity in a highly structured network. We utilized scat detection dogs (Canis lupus familiaris) as a means of collecting non-invasive genetic samples of American mink (Neovison vison) individuals and used spatial capture-recapture models (SCR) to gain inferences about mink population density and connectivity. Density of mink was not constant across the landscape, but rather increased with increasing distance from city, town, or village centers, and mink activity was associated with water. The SCR model allowed us to estimate the density and spatial distribution of individuals across a 388 km² area. The model was used to investigate patterns of space usage and to evaluate covariate effects on encounter probabilities, including differences between sexes. This study provides an application of capture-recapture models based on ecological distance, allowing us to directly estimate landscape connectivity. This approach should be widely applicable to provide simultaneous direct estimates of density, space usage, and landscape connectivity for many species.