We investigate the extent to which social ties between people can be inferred from co-occurrence in time and space: Given that two people have been in approximately the same geographic locale at approximately the same time, on multiple occasions, how likely are they to know each other? Furthermore, how does this likelihood depend on the spatial and temporal proximity of the co-occurrences? Such issues arise in data originating in both online and offline domains as well as settings that capture interfaces between online and offline behavior. Here we develop a framework for quantifying the answers to such questions, and we apply this framework to publicly available data from a social media site, finding that even a very small number of co-occurrences can result in a high empirical likelihood of a social tie. We then present probabilistic models showing how such large probabilities can arise from a natural model of proximity and co-occurrence in the presence of social ties. In addition to providing a method for establishing some of the first quantifiable estimates of these measures, our findings have potential privacy implications, particularly for the ways in which social structures can be inferred from public online records that capture individuals' physical locations over time.computer science | privacy | probabilistic models | social networks E very day, we make inferences about the social world from incomplete observations of events around us. A particular category of such inferences draws on co-occurrences in space and time-basing estimates of a social tie between two people on the fact that they were in the same geographic locale at roughly the same time. In addition to its intuitive accessibility, such reasoning has been employed in psychological studies of urban life (1) and legal analyses of the dangers of "guilt by association" (2, 3). These issues also arise naturally in online domains, including those that reflect spatio-temporal traces of their users' activities in the physical world. Despite the broad relevance of the underlying questions, however, there has been essentially no precise basis for quantifying the significance of these effects. Here we study this issue in an online setting and find that geographic co-occurrences can in fact have significant power in forming inferences about social ties: The knowledge that two people were proximate at just a few distinct locations at roughly the same times can indicate a high conditional probability that they are directly linked in the underlying social network, in the data we consider. Our results use publicly accessible spatial and temporal information from a large social media site to derive estimates of links in the online social network of the site. We also develop a probabilistic model to account for the high probabilities that are observed. In addition to providing a quantitative basis for the power of these inferences, our results have implications for the unintended leakage of private information via participation in such sites.Our analysis uses...