16. Randomly generate a graph using
Waxman’s method
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17. Each node is expanded to form a
random graph (transit domain)
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18. Connect stub domains to the transit
domain.
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19. Looks good, but is it
close to the real thing?
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20. “On Power-Law
Relationships of the
Internet Topology”quot;
The Faloutsos brothers,
SIGCOMM ‘99
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20
21. Use four traces of
Internet topology
collected between 97-98
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22. AS-Level Topology
Time
Num of Num of Max Average
Nodes
Edges
outdegree
outdegree
Nov 97
3015
5156
590
3.42
Apr 98
3520
6432
745
3.65
Dec 98
4398
8256
979
3.76
Router-Level Topology
1995
3888
5012
2.57
22
23. Observations: the graphs
can be decomposed into
two components: trees
and core.
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24. Connect stub domains to the transit
domain.
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25. 40-50%!
of the nodes are in trees
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26. 3!
maximum depth of trees
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27. 1!
depth of >80% of the
trees
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28. Time
Num of Num of Max Average
Nodes
Edges
outdegree
outdegree
Nov 97
3015
5156
590
3.42
Apr 98
3520
6432
745
3.65
Dec 98
4398
8256
979
3.76
Out-degree is highly
skewed!
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29. Let quot;
dv be the out-degree of a
node, and quot;
rv be the rank of a node
(i.e., index in the order of
decreasing outdegree)
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30. Plot dv versus rv on quot;
log-log scale
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47. Let quot;
P(h) be the number of
node pairs within h hops
of each otherquot;
(include self-pairs, count
every pair twice)
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48. P(0) = N
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49. P(1) = N + 2E
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50. P(δ) = N2quot;
where δ is the diameter of the graph
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51. Plot P(h) versus h on quot;
log-log scale
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61. It holds in 97-98.quot;
What about later?
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62. “Power-Laws and the AS-
Level Internet Topology”quot;
G. Siganos and the Faloutsos
brothers, IEEE/ACM TON
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74. Generating Power Law
Topology (simplified)
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74
75. “On the Original of Power
Laws in Internet Topologies”quot;
A Medina, I Matta, J Byers,quot;
ACM SIGCOMM, ‘00
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