Vertex overload breakdown in evolving networks

TL;DR

This paper investigates overload breakdowns in evolving scale-free networks, showing that vertex capacity must grow with network size to prevent avalanches, and explores the dynamics of giant component formation.

Contribution

It introduces a model of overload breakdown in evolving networks considering different load limitations and analyzes the conditions to prevent catastrophic failures.

Findings

Avalanche-like breakdowns occur under overload conditions.

Vertex capacity growth is necessary to prevent network avalanches.

Irregular dynamics observed in giant component formation.

Abstract

We study evolving networks based on the Barabasi-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanche-like breakdowns for both load limitations are observed. In order to avoid such avalanches we argue that the capacity of the vertices has to grow with the size of the system. An interesting irregular dynamics of the formation of the giant component (for the intrinsic communication activity case is also studied). Implications on the growth of the Internet is discussed.