Edge overload breakdown in evolving networks.

We investigate growing networks based on Barabási 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, like 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 by preferential attachment (as defines the Barabási 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.