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The structure of the Internet

The structure of the Internet. How are routers connected?. Why should we care? While communication protocols will work correctly on ANY topology ….they may not be efficient for some topologies Knowledge of the topology can aid in optimizing protocols. The Internet as a graph.

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The structure of the Internet

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  1. The structure of the Internet

  2. How are routers connected? • Why should we care? • While communication protocols will work correctly on ANY topology • ….they may not be efficient for some topologies • Knowledge of the topology can aid in optimizing protocols

  3. The Internet as a graph • Remember: the Internet is a collection of networks called autonomous systems (ASs) • The Internet graph: • The AS graph • Nodes: ASs, links: AS peering • The router level graph • Nodes: routers, links: fibers, cables, MW channels, etc. • How does it looks like?

  4. Poisson distribution Random graphs in Mathematics The Erdös-Rényi model • Generation: • create n nodes. • each possible link is added with probability p. • Number of links: np • If we want to keep the number of links linear, what happen to p as n?

  5. The Waxman model • Integrating distance with the E-R model • Generation • Spread n nodes on a large enough grid. • Pick a link uar and add it with prob. that exponentially decrease with its length • Stop if enough links • Heavily used in the 90s

  6. 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100

  7. The Faloutsos brothers Measured the Internet AS and router graphs. Mine, she looks different! Notre Dame Looked at complex system graphs: social relationship, actors, neurons, WWW Suggested a dynamic generation model 1999

  8. The Faloutsos Graph1995 Internet router topology3888 nodes, 5012 edges, <k>=2.57

  9. 25 2212 SCIENCE CITATION INDEX Nodes: papers Links: citations Witten-Sander PRL 1981 1736 PRL papers (1988) P(k) ~k- ( = 3) (S. Redner, 1998)

  10. Sex-web Nodes: people (Females; Males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. Liljeros et al. Nature 2001

  11. Web power-laws

  12. (2) The attachment is NOT uniform. A node is linked with higher probability to a node that already has a large number of links. Examples : WWW : new documents link to well known sites (CNN, YAHOO, NewYork Times, etc) Citation : well cited papers are more likely to be cited again SCALE-FREE NETWORKS (1) The number of nodes (N) is NOT fixed. Networks continuously expand by the addition of new nodes Examples: WWW : addition of new documents Citation : publication of new papers

  13. Scale-free model P(k) ~k-3 (1)GROWTH: At every timestep we add a new node with m edges (connected to the nodes already present in the system). (2)PREFERENTIAL ATTACHMENT :The probability Π that a new node will be connected to node i depends on the connectivity ki of that node A.-L.Barabási, R. Albert, Science 286, 509 (1999)

  14. The Faloutsos Graph

  15. The Internet Topology as a Jellyfish Shells: Core 1 • Core: High-degree clique • Shell: adjacent nodes of previous shell, except 1-degree nodes • 1-degree nodes: shown hanging • The denser the 1-degree node population the longer the stem 2 3

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