# Degree Dispersion Increases the Rate of Rare Events in Population Networks

## TL;DR

This paper demonstrates that greater degree dispersion in population networks universally amplifies the likelihood of rare, large fluctuations, such as extinction or switching, by an exponential factor related to degree variance.

## Contribution

It provides a theoretical framework linking degree dispersion to increased rates of rare events in population networks, supported by explicit calculations for key event types.

## Key findings

- Degree dispersion exponentially increases rare event rates.
- The increase is proportional to the variance over the mean squared of degree distribution.
- Results are applicable across different types of rare events in networks.

## Abstract

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 dispersion -- the fact that the number of local connections in networks varies broadly -- increases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network's degree distribution over its mean squared.