A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals1,2,3,4. Human society is based to a large extent on mechanisms that promote cooperation5,6,7. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs8,9,10,11,12,13,14,15,16,17. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks18,19,20,21,22,23,24. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks25,26: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of ‘social viscosity’ even in the absence of reputation effects or strategic complexity.