Edge overload breakdown in evolving networks

TL;DR

This paper studies how evolving scale-free networks with overload-sensitive edges, based on betweenness centrality, experience avalanching breakdowns during growth, with implications for real-world communication networks.

Contribution

It introduces a model of evolving networks with overload breakdowns sensitive to edge betweenness, highlighting differences between growth mechanisms.

Findings

Breakdowns occur after initial growth phase leading to fragmentation.

Random attachment results in less violent breakdowns than preferential attachment.

Constant average connections prevent breakdown avalanches.

Abstract

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.