Power Laws and Fragility in Flow Networks

TL;DR

This paper investigates flow networks, revealing that their tendency toward power law degree distributions results from their structure, and that such networks are more fragile to failures than non-flow networks.

Contribution

It introduces the first random graph model for flow networks with power law degree distributions independent of rich-get-richer mechanisms.

Findings

Flow networks tend to a power law degree distribution due to their structure.

Flow networks with power law distributions are more vulnerable to catastrophic failures.

The model explains the fragility of economic and ecological networks.

Abstract

What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by flow. We show that flow networks tend to the power law degree distribution (PLDD) due to a self-reinforcing process involving position within the global network structure, and thus present the first random graph model for PLDDs that does not depend on a rich-get-richer function of nodal degree. We also show that in contrast to non-flow networks, PLDD flow networks are dramatically more vulnerable to catastrophic failure than non-PLDD flow networks, a finding with potential explanatory power in our age of resource- and financial-interdependence and turbulence.