A number of peer$-$to$-$peer systems on the internet are based on

overlay networks. Rather than using the physical internet as the network on which to perform computation,

these systems run protocols by which nodes choose collections of virtual $$neighbors$$ so as to define a higherlevel graph whose structure may bear little or no relation to the underlying physical network. Such an overlay

network is then used for sharing data and services, and it can be extremely flexible compared with a physical

network, which is hard to modify in real time to adapt to changing conditions.