We investigated the social organization of the Australian sleepy lizard, Tiliqua rugosa, by describing the social network of a local population. We attached activity meters and GPS recorders to 21 neighbouring lizards in a semiarid site in South Australia, and monitored their location every 10 min over 3 months (September-December 2007). From over 5000 sets of synchronized location records we calculated distances between all possible dyads of active lizards, and constructed binary social networks based on close associations between individuals. We compared empirical networks with a null model network for spatially structured populations that assumed random movement within lizard home ranges. We showed significantly lower network degree (i.e. fewer cases of individuals associating) in the observed network than in the null model, and deduced avoidance between some individuals. We found the predominant form of social organization was pair living, and, contrary to previous reports, we found pair associations persisted after mating had finished. Thus, the network analysis revealed a cryptic social organization, which cannot be explained by either biparental care or mate guarding, but may instead relate to refuge site distributions, enhanced vigilance or efficient location of mates in subsequent seasons.