The Science of Complex Networks and the Internet: Lies, Damned Lies, and Statistics. Walter Willinger AT&T Labs-Research [email protected] Outline. The Science of Complex Networks (“Network Science”) What “Network Science” has to say about the Internet
“The study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena.” (National Research Council Report, 2006)
“To develop a body of rigorous results that will improve the predictability of the engineering design of complex networks and also speed up basic research in a variety of applications areas.” (National Research Council Report, 2006)
To what extent does there exist a “network structure” that is
responsible for large-scale properties in complex systems?
Are there “universal laws” governing the structure (and
resulting behavior) of complex networks? To what extent is
self-organization responsible for the emergence of system
features not explained from a traditional (i.e., reductionist)
How can one assess the vulnerabilities or fragilities
inherent in these complex networks in order to avoid
“rare yet catastrophic” disasters? More practically,
how should one design, organize, build, and manage
Most Cited Publications in Network Science Literature (As recorded by the Web of Science1 on October 1, 2007; courtesy D. Alderson)
I will show that in the case of the Internet …
The application of “Network Science” in its current form has led to conclusions that are not controversial but simply wrong.
I will deconstruct the existing arguments and generalize the potential pitfalls common to “Network Science.”
I will also be constructive and illustrate an alternative approach to “Network Science” based on engineering considerations.
A few nodes have lots of connections
Source: Faloutsos et al (1999)
Most nodes have few connections
Cover Story: Nature 406, 2000. (cont.)
U.S. Electrical Power Grid (cont.)
Basic Question (cont.)
Do the available Internet-related connectivity
measurements and their analysis support the sort
of claims that can be found in the existing complex
high BW low degree
high degree low BW
15 x 1-port 10 GE
15 x 3-port 1 GE
15 x 4-port OC12
15 x 8-port FE
10Router Technology Constraint
Cisco 12416 GSR, circa 2002
U. So. Florida
U. So. Miss.
(as of August 2004)
OC-3 (155 Mb/s) Bender)
OC-12 (622 Mb/s)
GE (1 Gb/s)
OC-48 (2.5 Gb/s)
10GE (10 Gb/s)
CENIC Backbone (as of January 2004)
The Corporation for Education Network Initiatives in California (CENIC) acts as ISP for the state's colleges and universities
Back to the Basic Question: Bender)
Do the available Internet-related connectivity measurements
and their analysis support the sort of claims that can be
found in the existing complex networks literature?
Short Answer: No!
Step 1 Bender): Constrain to be feasible
Step 2: pick traffic demand model
Abstracted Technologically Feasible Region
Step 3: Compute max flow
1000Heuristically Optimized Topologies (HOT)
Given realistic technology constraints on routers, how well is the network able to carry traffic?
Hosts Bender)HOT Design Principles
Mesh-like core of fast, low degree routers
High degree nodes are at the edges.
HOT- vs. PA-type Network Models Bender)
Fast, low degree
Slow, high degree
High degree nodes
“When exactitude is elusive, it is better to be approximately right than certifiably wrong.”