Current tests for contagion in social network studies are vulnerable to the confounding effects of latent homophily (i.e., ties form preferentially between individuals with similar hidden traits). We demonstrate a general method to lower bound the strength of causal effects in observational social network studies, even in the presence of arbitrary, unobserved individual traits. Our tests require no parametric assumptions and each test is associated with an algebraic proof. We demonstrate the effectiveness of our approach by correctly deducing the causal effects for examples previously shown to expose defects in existing methodology. Finally, we discuss preliminary results on data taken from the Framingham Heart Study.