Social insect colonies demonstrate some of the most striking social behaviours that are seen in nature. Social interaction in these species defines their behaviour and has a large impact on their success. A number of ant species organise their colony over several socially interacting, but spatially separated nests. This behaviour is known as polydomy. I used simulation modelling to investigate the costs and benefits of this behaviour. The results showed that colony organisation interacts with both foraging strategy and resource distribution to determine the effect of polydomy on foraging success. Importantly, I show that there are previously undiscussed costs to polydomy. I also addressed questions of how the social connections between the nests in a colony are organised. Complex interacting systems such as the trail system formed between nests in a polydomous colony can be represented as a network. I review the use of this representation in studies of social insects and provide suggestions for future studies on how social insect systems may provide insight into the construction and use of effective network systems in general. By representing the trail systems found between nests as networks I show that the systems formed by ants are highly efficient for the transportation of resources but balance this efficiency with the cost of producing trails. A number of simple mechanisms have been proposed for the construction of these networks. I test these theories and show that the simplest mechanisms suggested may not be sufficient to replicate the natural systems. This thesis contributes to the understanding of the behaviour of ants in polydomous colonies and to the understanding of distributed biological systems more generally. The work also provides a basis for future research on how efficient systems can be constructed using simple rules.