Editing Small-world network (section)

==Network robustness==
It is hypothesized by some researchers, such as [[Albert-László Barabási]], that the prevalence of small world networks in biological systems may reflect an evolutionary advantage of such an architecture. One possibility is that small-world networks are more robust to perturbations than other network architectures. If this were the case, it would provide an advantage to biological systems that are subject to damage by [[mutation]] or [[virus|viral infection]].

In a small world network with a degree distribution following a [[power-law]], deletion of a random node rarely causes a dramatic increase in [[mean-shortest path]] length (or a dramatic decrease in the [[clustering coefficient]]). This follows from the fact that most shortest paths between nodes flow through [[Hub (network science)|hubs]], and if a peripheral node is deleted it is unlikely to interfere with passage between other peripheral nodes. As the fraction of peripheral nodes in a small world network is much higher than the fraction of [[spoke–hub distribution paradigm|hubs]], the probability of deleting an important node is very low. For example, if the small airport in [[Sun Valley, Idaho]] was shut down, it would not increase the average number of flights that other passengers traveling in the United States would have to take to arrive at their respective destinations. However, if random deletion of a node hits a hub by chance, the average path length can increase dramatically. This can be observed annually when northern hub airports, such as Chicago's [[O'Hare International Airport|O'Hare airport]], are shut down because of snow; many people have to take additional flights.

By contrast, in a random network, in which all nodes have roughly the same number of connections, deleting a random node is likely to increase the mean-shortest path length slightly but significantly for almost any node deleted. In this sense, random networks are vulnerable to random perturbations, whereas small-world networks are robust. However, small-world networks are vulnerable to targeted attack of hubs, whereas random networks cannot be targeted for catastrophic failure.