Fission-fusion dynamics allow for the costs and benefits of sociality to be regulated through changes in group size. There are different modal fission-fusion societies, and female Asian and African elephant populations examined so far have shown different social structures and average group sizes. We report on female Asian elephant social structure in Nagarahole and Bandipur National Parks (Kabini population), southern India, and examine the role of group size in affecting the outcome of social structure analysis in female elephants. Based on five years of data, we found the Kabini association network structured into highly modular communities that we call clans. A comparison of the Kabini dataset, modified to match sampling methods, with previously published Uda Walawe Asian elephant and Samburu African elephant data showed that measures of association and network structure were more similar amongst the Asian elephant populations compared to Samburu. The Samburu population formed a hierarchically-nested multilevel society whereas the Asian populations did not. However, we found hierarchical levels in all three populations using Louvain community detection. Moreover, the average community sizes obtained through the Louvain method were not significantly different across populations, indicating basic similarities in social structure. We examined the effect of average group size on association and network statistics. Higher average association index and degree, and lower average path length in Samburu compared to Kabini were explained by larger average group size in Samburu. Thus, underlying similarities in the social networks of species showing fission-fusion dynamics may be obscured by differences in average group size.