Over the past decade network theory has been applied successfully to the study of a variety of complex adaptive systems. However, the application of these techniques to non-human social networks has several shortfalls. Firstly, in most cases the strength of associations between individuals is disregarded. Secondly, present techniques assume that observed interactions are invariant values and not statistical samples taken from a population. These two simplifications have weakened the value of these techniques when applied to the study of animal social systems. Here we introduce a set of behaviorally meaningful weighted network statistics that can be readily applied to matrices of association indices between pairs of individual animals. We also introduce bootstrapping techniques that estimate the effects of sampling uncertainty on the network statistics and structure. Finally, we discuss the use of randomisation tests to detect the departure of observed network statistics from expected values under null hypotheses of random association given the sampling structure of the data. We use two case studies to show that these techniques provide invaluable insight in the dynamics of interactions within social units and in the community structure of societies. ; Comment: 13 pages, 3 figures. published in Animal Behaviour