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There is great interest in predicting rare and extreme events in complexsystems, and in particular, understanding the role of network topology infacilitating such events. In this work, we show that degree dispersion -- thefact that the number of local connections in networks varies broadly --increases the probability of large, rare fluctuations in population networksgenerically. We perform explicit calculations for two canonical and distinctclasses of rare events: network extinction and switching. When the distance tothreshold is held constant, and hence stochastic effects are fairly comparedamong networks, we show that there is a universal, exponential increase in therate of rare events proportional to the variance of a network's degreedistribution over its mean squared.

Degree Dispersion Increases the Rate of Rare Events in Population Networks