1. Networks are being increasingly used to quantify interaction patterns of a broad range of social systems ranging from solitary to eusocial species. Social behavior driving the complexity of interaction networks has important consequences towards infectious disease transmission. 2. Prior studies however have been species and population specific, which highlights the need to develop a general theory towards the implications of social behavior on disease risk. 3. We used quantitative tools to review the commonalities and differences in the structure of 666 published interaction networks from 47 non-human species categorized into four social systems - relatively solitary, fission-fusion, social and socially hierarchical species. Additionally, we determined the disease costs of sociality due to the underlying interaction network structure. 4. We found that the interaction networks of solitary species have the highest variation in individual social partners, while the interaction networks of fission-fusion species were the most fragmented. 5. Disease simulations show that the structure of interaction networks can alleviate the disease costs of group living for social, but not socially hierarchical species. 6. We also find clear differences between the four social systems in terms of behavioral plasticity of individuals towards increasing group size. Socially hierarchical species maintained network connectivity with increasing group size, whereas non-hierarchical social species reduced effort towards each pairwise interaction to offset the higher amount of energy invested in engaging with new social partners. 7. Our findings offer new perspective on the debate about the disease costs of group living by evaluating how social organization strategies mediate pathogen pressures.