Land use change and biological invasions collectively threaten biodiversity. Yet, few studies have addressed how altering the landscape structure and nutrient supply can promote biological invasions and particularly invasive spread (the spread of an invader from the place of introduction), or asked whether and how these factors interact with biotic interactions and invader properties. We here bridge this knowledge gap by providing a holistic network-based approach. Our approach combines a trophic network model with a spatial network model allowing us to test which combinations of abiotic and biotic factors can facilitate invasions and in particular invasive spread in food webs. We numerically simulated 6300 single-species invasions in clustered and random landscapes at different levels of nutrient supply. In total, our simulation experiment yielded 69\% successful invasions---71% in clustered landscapes and 66% in random landscapes, with the proportion of successful invasions increasing with nutrient supply. However, invasive spread was generally higher in random than in clustered landscapes. The latter can facilitate invasive spread within a habitat cluster, but prevent invasive spread between clusters. Low nutrient levels generally prevented the establishment of invasive species and their subsequent spread. However, successful invaders could have more severe impacts as they contribute more to total biomass density and species richness under such conditions. Good dispersal abilities drive the broad-scale spread of invasive species in fragmented landscapes. Our approach makes an important contribution towards a better understanding of what combination of landscape and invader properties can facilitate or prevent invasive spread in natural ecosystems. This should allow ecologists to more effectively predict and manage biological invasions.