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# B sfnet a graph having the most preferential

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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 overall bandwidth. • 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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## This document was uploaded on 03/12/2014 for the course CSCI 289 at UC Davis.

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