Nature realizes stable biodiversity, even though it escapes naive theoretical predictions. Coexistence of competing species is known to be facilitated by, for example, structured populations, heterogeneous individuals, and heterogeneous environments, which in one way or another allow different species to survive in a segregated manner. In reality, individuals disperse and interact with each other, often on networks of habitats connected in complex ways. We examine how heterogeneous degree distributions of networks, namely, heterogeneous contact rates for different habitats, influence stability of biodiversity. We show that heterogeneous networks induce stable coexistence of many species in cyclic competition, whereas well-mixed populations do not sustain coexistence. Coexistence based on networks does not require heterogeneity in environments or phenotypes, or spatially structured populations. Together with other mechanisms, the effect of heterogeneous networks may underly stable biodiversity in the real world. This event is part of the Program for Evolutionary Dynamics Seminar Series.