Section 1

Till 1999, people had faith in the structural generators, because they tried to assume and produce the heirarchical nature of the Internet.

In 1999, Faloustsos et al. declared that at the router and AS level, node degree distributions closely followed the Power Law.



Node degree is a local property. This paper is concerned about the large scale structure. It argues that local properties and large scale

structure are seperable, with some examples. The scaling performance of protocols is affected more by the large scale structure of the Internet than by local properties



So it is still an open question which generators best models the Internet for simulation purposes.



1st question:

To answer these questions, first of all what is the Internet ?

Two reps are used: AS level and router level. Three topology metrics are used to describe the graphs ( out of initial 8 ). characterizing network topologies is an important area where more work is needed.



Their results:

1. AS and router level graphs have similiar properties: Unpredictable at first !

2. At both levels, degree-based generators better model the Internet ! even though they ignore heirarchy. Paradoxical !



2nd question:

How does this happen ?

They find out that the power law distribution of degrees itself results in a loose form of hierarchy, between the strict hierarchy of structural generators and random graphs. They introduce a measure of heirarchy to describe and study these.



Thus the degree based generators win ! (because Power law generators result in a hierarhcical topology close to the Internet )



2. Related Work



Some metrics used by Medina et al.

Power law exponents of the degree distribution

degree rank

hop-plot

eigenvalue distribution



Real world graphs are well-modeled by Weibull distribution. Degree distribution of the AS Graph devitates significantly from a strict power-law fit. The essence is that the degree distribution is heavy tailed.



Impact of topology on performance: mainly in context of multicast



Section 3: Different Networks and Metrics