Plant–animal mutualistic networks are characterized by highly heterogeneous degree distributions. The majority of species interact with few partner species, while a small number are highly connected to form network hubs that are proposed to play an important role in community stability. It has not been investigated, however, if or how the degree distributions vary among types of mutualisms or communities, or between plants and animals in the same network. Here, we evaluate the degree distributions of pollination and seed-dispersal networks, which are two major types of mutualistic networks that have often been discussed in parallel, using an index based on Pielou's evenness. Among 56 pollination networks we found strong negative correlation of the heterogeneity between plants and animals, and geographical shifts of network hubs from plants in temperate regions to animals in the tropics. For 28 seed-dispersal networks, by contrast, the correlation was positive, and there is no comparable geographical pattern. These results may be explained by evolution towards specialization in the presence of context-dependent costs that occur if plants share the animal species as interaction partner. How the identity of network hubs affects the stability and resilience of the community is an important question for future studies.