A switch in specificity of avian influenza A viruses' hemagglutinin (HA) from avian-like (alpha2-3 sialylated glycans) to human-like (alpha2-6 sialylated glycans) receptors is believed to be associated with their adaptation to infect humans. We show that a characteristic structural topology--and not the alpha2-6 linkage itself--enables specific binding of HA to alpha2-6 sialylated glycans and that recognition of this topology may be critical for adaptation of HA to bind glycans in the upper respiratory tract of humans. An integrated biochemical, analytical and data mining approach demonstrates that HAs from the human-adapted H1N1 and H3N2 viruses, but not H5N1 (bird flu) viruses, specifically bind to long alpha2-6 sialylated glycans with this topology. This could explain why H5N1 viruses have not yet gained a foothold in the human population. Our findings will enable the development of additional strategies for effective surveillance and potential therapeutic interventions for H5N1 and possibly other influenza A viruses.