Degree heterogeneity increases the probability of rare events in population networks

There is great interest in predicting rare and extreme events in complex systems, and in particular,
understanding the role of network topology in facilitating such events. In this work, we show that
degree heterogeneity - the fact that the number of local connections in complex networks is broadly
distributed - increases the probability of large, rare fluctuations in population networks generically.
We perform explicit calculations for two canonical examples of rare events: network extinction and
switching. When the distance to bifurcation is held constant, and hence stochastic effects are fairly
compared among networks, we show that the probability exponent for rare events decreases linearly
with the ratio of the degree distribution's standard deviation to its mean.