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Unformatted text preview: e in real Internet.
• So people jumped on the “preferential attachment” bandwagon. Degree distribution – not the whole story Fig. 1. Diversity among graphs having the same degree sequence D. (a) RNDnet: a network consistent with construction by PA. The two networks represent
the same graph, but the ﬁgure on the right is redrawn to emphasize the role that high-degree hubs play in overall network connectivity. (b) SFnet: a graph having
the most preferential connectivity, again drawn both as an incremental growth type of network and in a form that emphasizes the importance of high-degree
nodes. (c) BADNet: a poorly designed network with overall connectivity constructed from a chain of vertices. (d) HOTnet: a graph constructed to be a simpliﬁed
version of the Abilene network shown in Fig. 2. (e) Power-law degree sequence D for networks shown in a–d. Only di 1 is shown. the resulting models are widely conjectured to be asymptotically
equivalent (e.g., see ref. 6 and references therein).
In particular, for a g raph g hav ing deg ree sequence D, we
define the purely g raph-theoretic quantit y s(g)
(i, j) E(g)d id j,
where E(g) is the set of edges in the graph. It is easy to check that
high s(g) requires high-degree vertices to c onnect to other graph, even the relatively most likely, is actually unlikely in absolute
terms to be selected. The graphs in Fig. 1 c and d have the values
S(gc) 0.33 and S(gd) 0.34, respectively; furthermore, there are
relatively few graphs with S values this low, and thus any graphs
similar to these are vanishingly unlikely to arise at random (6). The
remainder of this article explains in more detail why the underlying “First principles” – start with constraints on routers Cisco router w 15 slots • Set number of interface cards. Initially with each new card added, increase
• Once number of connections exceeds interface cards, connections have to
share limited bandwidth. (Increase connectivity and decrease maximum
bandwidth available to each link.)
• Overhead in switching causes decrease in total bandwidth. “Core” versus “edge”
• Core routers – support highest lin...
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- Winter '11