Broadcast network media such as Ethernet presents interesting problems for link state protocols, both in terms of database synchronization and SPF calculations. Think of six routers sharing a broadcast link, as in Figure 4.22. If each of the six routers forms an adjacency with each of its neighbors in the link, there will be a total of 15 adjacencies, as shown in the illustration. In fact the number of adjacencies that will be formed under such a scenario, given some number of routers n, is .5(n^{2}—n). What this formula tells you is that as the number of routers sharing a broadcast link increases, the number of adjacencies increases exponentially.

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