  The Lotka-Volterra system is a set of ordinary differential equations
describing growth of interacting ecological species. This model has gained
renewed interest in the context of random interaction networks. One of the
debated questions is understanding how the number of species in the system,
$n$, influences the stability of the model. Robert May demonstrated that large
systems become unstable, unless species-species interactions vanish. This
outcome has frequently been interpreted as a universal phenomenon and
summarised as "large systems are unstable". However, May's results were
performed on a specific type of graphs (Erd\H{o}s-R\'enyi), whereas we explore
a different class of networks and we show that the competitive Lotka-Volterra
system maintains stability even in the limit of large $n$, despite
non-vanishing interaction strength. We establish a lower bound on the
interspecific interaction strength, formulated in terms of the maximum and
minimum degrees of the ecological network, rather than being dependent upon the
network's size. For values below this threshold, coexistence of all species is
attained in the asymptotic limit. In other words, the outlier nodes with large
degree cause instability, rather than the large number of species in the
system. Our result refines May's bound, by showing that the type of network
model is relevant and can lead to completely different results.
