A Study On Directed Internet Graphs

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A Study On Directed Internet Graphs

• by Priya Mandawat

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The Objective

• To survey the existing techniques for logical
  relationship inference and hierarchical
  classification of Internet graphs
• To investigate properties that characterize the
  directed graph representation of the Internet
  topology

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Motivation

• Undirected graphs do not provide a complete
  picture with regard to traffic flow
  (Applications Content Distribution Networks)
• Simulations require synthetically generated
  topologies that accurately represent the Internet

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RoadMap

• Background (Undirected Graphs)
• Previous Work (Directed Graphs)
• Properties of Directed Internet Graphs
• Experiments
• Conclusions
• Future Work

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The Undirected Internet Graphs

• Properties
• Node degree and other metrics follow power laws
  Faloutsos et al.
• Growth Model
• Internet graphs exhibit preferential connectivity
  Barabasi et al.
• Graph Generators
• PLRG, GLP, Inet, Brite etc
• Evaluation
• Comparison of graph generators- Tian Bu Don
  Towsely

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Previous Work on Directed Internet Graphs

• Inference of Logical Relationships in the
  connectivity graph
• Hierarchical Classification of ASes

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Inference of Logical Relationships

• The Problem To assign a relationship to each
  pair of ASes that share an edge in the undirected
  topology graph
• L. Gao. On Inferring Autonomous System
  Relationships in the Internet. In IEEE/ACM Trans.
  Networking, December 2001.
• L. Subramanian, S. Agarwal, J. Rexford, and R. H.
  Katz. Characterizing the Internet Hierarchy from
  Multiple Vantage Points. In Proc. IEEE INFOCOM,
  June 2002.
• J. Xia and L. Gao. On Evaluation of AS
  Relationship Inferences. In Proc. IEEE Globecom
  2004.

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Highlights

• Peer-to-Peer relationships are hard to classify

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Hierarchical Classification of ASes

• The Problem To divide the directed internet
  topology graph into a hierarchy naturally imposed
  by the directivity and assign each AS to a
  particular layer
• Z. Ge, D. Figueiredo, S. Jaiwal, and L. Gao, On
  the hierarchical structure of the logical
  Internet graph, in Proc. SPIE ITCOM, August
  2001.
• L. Subramanian, S. Agarwal, J. Rexford, and R. H.
  Katz. Characterizing the Internet Hierarchy from
  Multiple Vantage Points. In Proc. IEEE INFOCOM,
  June 2002.

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Highlights

• How to classify an AS that has parents at
  different levels?

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Experiments

• Objective To check for the existence of
  properties/trends in directed Internet topology
  graphs
• Method
• Obtained relationship inference data by
• Running Gaos algorithm on Route Views dataset
• Running Georgos algorithm on the IRR dataset
• Plotted and analyzed graphs on the above data

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Properties of Directed Internet Graphs

• In-Degree Vs Out-Degree
• In-Degree Vs Peers
• of customers Vs of providers

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In-Degree Vs Out-Degree
On an average, In-degree and Out-degree are
inversely related On an average, Top-tier has
maximum customers
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In-Degree Vs Out-Degree (contd.)
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In-degree Vs Peers
Top-tier does not have maximum peering
relationships
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In-degree Vs Peers (contd.)
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of customers Vs of providers
90 of the customers have less than 3 providers
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of customers Vs of providers (contd.)
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Conclusions

• Reviewed existing techniques for inference of
  logical relationships and hierarchical
  classification on directed graphs
• Described interesting properties observed in
  directed Internet graphs

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Future Work

• To use different datasets/algorithms to verify
  the existence of the earlier mentioned properties
• To analyze the properties that characterize a
  good hierarchy and to evaluate existing
  hierarchical classification algorithms based on
  them

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Acknowledgements

• Special Thanks to Georgos Signos and Yihua He for
  their help with the Datasets and incidental
  technical glitches!

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Thank you!