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, which show high fission-fusion dynamics. Based on five years of data, we found the Kabini association network structured into highly modular communities that we call clans. We then modified the dataset (to obtain the Kabini 500-m dataset) to match sampling methods previously used in a study each of Asian (Uda Walawe) and African savannah (Samburu) elephants, so that network and association statistics could be compared across populations. Measures of association and network structure previously used 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 clustering 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. Since fission-fusion dynamics allow for community members to form groups of different sizes, 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 the Kabini 500-m dataset were explained by the 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.