1. The Science of Complex Networks and the Internet: Lies, Damned Lies, and Statistics Walter Willinger AT&T Labs-Research walter@research.att.com

2. 2 Outline The Science of Complex Networks (“Network Science”) What “Network Science” has to say about the Internet What “engineering” has to say about the Internet Engineered vs. random network models Implications

3. 3 Acknowledgments John Doyle (Caltech) David Alderson (Naval Postgraduate School) Steven Low (Caltech) Yin Zhang (Univ. of Texas at Austin) Matthew Roughan (U. Adelaide, Australia) Anja Feldmann (TU Berlin) Lixia Zhang (UCLA) Reza Rejaie (Univ. of Oregon) Mauro Maggioni (Duke Univ.) Bala Krishnamurthy, Alex Gerber, Shubho Sen, Dan Pai (AT&T) … and many of their students and postdocs

4. 4 NETWORK SCIENCE http://www.nap.edu/catalog/11516.html “First, networks lie at the core of the economic, political, and social fabric of the 21st century.” “Second, the current state of knowledge about the structure, dynamics, and behaviors of both large infrastructure networks and vital social networks at all scales is primitive.” “Third, the United States is not on track to consolidate the information that already exists about the science of large, complex networks, much less to develop the knowledge that will be needed to design the networks envisaged…” January, 2006

5. 5 “Network Science” in Theory … What? “The study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena.” (National Research Council Report, 2006) Why? “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) Who? –Physicists (statistical physics), mathematicians (graph theory), computer scientists (algorithm design), etc.

6. 6 Basic Questions ask by Network Scientists Question 1 To what extent does there exist a “network structure” that is responsible for large-scale properties in complex systems? Performance Robustness Adaptability / Evolvability “Complexity”

7. 7 Basic Questions ask by Network Scientists (cont.) Question 2 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) viewpoint?

8. 8 Basic Questions ask by Network Scientists (cont.) Question 3 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 complex networks?

9. 9 Observation The questions motivating recent work in “Network Science” are “the right questions” –network structure and function –technological, social, and biological The issue is whether or not “Network Science” in its current form has been successful in providing scientifically solid answers to these (and and other) questions. Our litmus test for examining this issue –Applications of the current “Network Science” approach to real systems of interest (e.g., Internet)

10. 10 As scientists, why should we care? “Network Science” as a new scientific discipline …

11. 11 Publications in Network Science Literature by Discipline (As recorded by the Web of Science 1 on October 1, 2007; courtesy D. Alderson)

12. 12 Articlecites 1. Watts, DJ; Strogatz, SH. 1998. Collective dynamics of 'small-world' networks, NATURE 393(668).2244 2. Barabasi AL, Albert R. 1999. Emergence of scaling in random networks. SCIENCE 286 (543).2110 3. Albert R, Barabasi AL. 2002. Statistical Mechanics of Complex Networks. REV. OF MODERN PHYSICS 74 (1).1972 4. Newman MEJ. 2003. The structure and function of complex networks. SIAM REVIEW 45 (2).960 5. Jeong H, Tombor B, Albert R, et al. 2000. The large-scale organization of metabolic networks. NATURE 407 (6804). 903 6. Strogatz, SH. 2001. Exploring complex networks, NATURE 410(6825).884 7. Albert R, Jeong H, Barabasi AL. 2000. Error and attack tolerance of complex networks. NATURE 406 (6794).747 8. Dorogovtsev SN, Mendes JFF. 2002. Evolution of networks. ADV IN PHYSICS 51 (4).636 9. Giot, L; Bader, J.S.; Brouwer, C; Chaudhuri, A; Kuang, B; et al. 2003. A protein interaction map of Drosophila melanogaster, SCIENCE, 302(5651). 550 10. Milo, R; Shen-Orr, S; Itzkovitz, S; Kashtan, N; Chklovskii, D; Alon, U. 2002. Network motifs: Simple building blocks of complex networks, SCIENCE 298(5594). 489 11. Amaral LAN, et al. 2000. Classes of small-world networks. PROC. NAT. ACAD. SCI. 97 (21).475 12. Ravasz, E; Somera, AL; Mongru, DA; Oltvai, ZN; Barbasi, AL. 2002. Hierarchical organization of modularity in metabolic networks, SCIENCE 297(5586). 457 13. Pastor-Satorras, R; Vespignani, A. 2001. Epidemic spreading in scale-free networks, PHYS. REV. LETT. 86(14).440 14. Tong, AHY, et al. 2004. Global mapping of the yeast genetic interaction network. SCIENCE 303(5659)412 15. Barabasi, AL; Albert, R; Jeong, H. 1999. Mean-field theory for scale-free random networks, PHYSICA A 272. 364 13279 Most Cited Publications in Network Science Literature (As recorded by the Web of Science 1 on October 1, 2007; courtesy D. Alderson)

13. 13 As scientists, why should we care? “Network Science” as a new scientific discipline … “Network Science” for the masses …

14. 14 The “New Science of Networks”

15. 15 As scientists, why should we care? “Network Science” as a new scientific discipline … “Network Science” for the masses … “Network Science” for the (Internet) experts …

16. 16 The “New Science of Networks”

17. 17 As scientists, why should we care? “Network Science” as a new scientific discipline … “Network Science” for the masses … “Network Science” for the Internet experts … “Network Science” for undergraduate/graduate students in Computer Science/Electrical Engineering

18. 18 The “New Science of Networks” New course offerings –http://www.cc.gatech.edu/classes/AY2010/cs8803 ns_fall/http://www.cc.gatech.edu/classes/AY2010/cs8803 ns_fall/ –http://www.netscience.usma.edu/about.phphttp://www.netscience.usma.edu/about.php –http://nicomedia.math.upatras.gr/courses/mnets/in dex_en.htmlhttp://nicomedia.math.upatras.gr/courses/mnets/in dex_en.html –http://www- personal.umich.edu/~mejn/courses/2004/cscs535 /index.htmlhttp://www- personal.umich.edu/~mejn/courses/2004/cscs535 /index.html –http://www.phys.psu.edu/~ralbert/phys597_09-fallhttp://www.phys.psu.edu/~ralbert/phys597_09-fall

19. 19 As scientists, why should we care? “Network Science” as a new scientific discipline … “Network Science” for the masses … “Network Science” for the Internet experts … “Network Science” for undergraduate/graduate students in Computer Science/Electrical Engineering … and most importantly, because we want to know how serious a science “Network Science” is ….

20. 20 The Main Points of this Talk … 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.

21. 21 What does “Network Science” say about the Internet Illustration with a case study –Problem: Internet router-level topology –Approach: Measurement-based –Result: Predictive models with far-reaching implications Textbook example for the power of “Network Science” –Appears solid and rigorous –Appealing approach with surprising findings –Directly applicable to other domains

22. 22 What does “Network Science” say about the Internet Measurement technique –traceroute tool –traceroute discovers compliant (i.e., IP) routers along path between selected network host computers

23. 23 Running traceroute: Basic Experiment Basic “experiment” –Select a source and destination –Run traceroute tool Example –Run traceroute from my machine in Florham Park, NJ, USA to www.duke.edu

24. Running “traceroute www.duke.edu” from NJ 1 fp-core.research.att.com (135.207.16.1) 2 ms 1 ms 1 ms 2 ngx19.research.att.com (135.207.1.19) 1 ms 0 ms 0 ms 3 12.106.32.1 1 ms 1 ms 1 ms 4 12.119.12.73 2 ms 2 ms 2 ms 5 tbr1.n54ny.ip.att.net (12.123.219.129) 4 ms 5 ms 3 ms 6 ggr7.n54ny.ip.att.net (12.122.88.21) 3 ms 3 ms 3 ms 7 192.205.35.98 4 ms 4 ms 8 ms 8 jfk-core-02.inet.qwest.net (205.171.30.5) 3 ms 3 ms 4 ms 9 dca-core-01.inet.qwest.net (67.14.6.201) 11 ms 11 ms 11 ms 10 dca-edge-04.inet.qwest.net (205.171.9.98) 11 ms 15 ms 11 ms 11 gw-dc-mcnc.ncren.net (63.148.128.122) 18 ms 18 ms 18 ms 12 rlgh7600-gw-to-rlgh1-gw.ncren.net (128.109.70.38) 18 ms 18 ms 18 ms 13 roti-gw-to-rlgh7600-gw.ncren.net (128.109.70.18) 20 ms 20 ms 20 ms 14 art1sp-tel1sp.netcom.duke.edu (152.3.219.118) 23 ms 20 ms 20 ms 15 webhost-lb-01.oit.duke.edu (152.3.189.3) 21 ms 38 ms 20 ms 24

25. 25 traceroute-paths: (many) source-destination pairs

26. 26 What does “Network Science” say about the Internet Measurement technique –traceroute tool –traceroute discovers compliant (i.e., IP) routers along path between selected network host computers Available data: from large-scale traceroute experiments –Pansiot and Grad (router-level, around 1995, France) –Cheswick and Burch (mapping project 1997--, Bell-Labs) –Mercator (router-level, around 1999, USC/ISI) –Skitter (ongoing mapping project, CAIDA/UCSD) –Rocketfuel (state-of-the-art router-level maps of individual ISPs, UW Seattle) –Dimes (ongoing EU project)

27. 27 http://research.lumeta.com/ches/map/

28. 28 http://www.isi.edu/scan/mercator/mercator.html

29. 29 http://www.caida.org/tools/measurement/skitter/

30. 30 http://www.cs.washington.edu/research/networking/rocketfuel/bb

31. 31 http://www.cs.washington.edu/research/networking/rocketfuel/

32. 32 What does “Network Science” say about the Internet (cont.) Inference –Given: traceroute-based map (graph) of the router- level Internet (Internet service provider) –Wanted: Metric/statistics that characterizes the inferred connectivity maps –Main metric: Node degree distribution

33. 33 http://www.isi.edu/scan/mercator/mercator.html

34. 34 What does “Network Science” say about the Internet (cont.) Inference –Given: traceroute-based map (graph) of the router- level Internet (Internet service provider) –Wanted: Metric/statistics that characterizes the inferred connectivity maps –Main metric: Node degree distribution Surprising finding –Inferred node degree distributions follow a power law –A few nodes have a huge degree, while the majority of nodes have a small degree

35. 35 Power Laws and Internet Topology Source: Faloutsos et al (1999) Most nodes have few connections A few nodes have lots of connections

36. 36 What does “Network Science” say about the Internet (cont.) Inference –Given: traceroute-based map (graph) of the router- level Internet (Internet service provider) –Wanted: Metric/statistics that characterizes the inferred connectivity maps –Main metric: Node degree distribution Surprising finding –Inferred node degree distributions follow a power law –A few nodes have a huge degree, while the majority of nodes have a small degree Motivation for developing new network/graph models –Dominant graph models: Erdos-Renyi random graphs –But: Node degrees of Erdos-Renyi random graph models follow a Poisson distribution

37. 37 What does “Network Science” say about the Internet (cont.) New class of network models –Preferential attachment (PA) growth model Incremental growth: New nodes/links are added one at a time Preferential attachment: a new node is more likely to connect to an already highly connected node (p(k)  degree of node k) –Captures popular notion of “the rich get richer” –There exist many variants of this basic PA model –Generally referred to as “scale-free” network models Key features of PA-type network models –Randomness enters via attachment mechanism –Exhibit power law node degree distributions

38. 38 PA-type Networks

39. 39 What does “Network Science” say about the Internet (cont.) Model validation –The models “fit the data” because they reproduce the observed node degree distributions –The models are simple and parsimonious PA-type models have resulted in highly publicized claims about the Internet and its properties –High-degree nodes form a hub-like core –Fragile/vulnerable to targeted node removal –Achilles’ heel –Zero epidemic threshold

40. 40 Cover Story: Nature 406, 2000.

41. 41 Beyond the Internet … Social networks Information networks Biological networks Technological networks –U.S. electrical power grid (data source: FEMA)

42. 42

43. 43 U.S. Electrical Power Grid

44. 44 Beyond the Internet … Social networks Information networks Biological networks Technological networks –U.S. electrical power grid (data source: FEMA) –Western U.S. power grid: 4921 nodes, 6594 links –J.-W. Wang and L.-L. Rong, “Cascade-based attack vulnerability on the US power grid,” Safety Science 47, 2009 –NYT article, April 18, 2010: “Academic paper in China sets off alarms in U.S.” Interdependent networks (e.g., Internet and power grid) –S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley and S. Havlin, “Catastrophic cascade of failures in interdependent networks”, Nature 464 (April 2010)

45. 45 On the Impact of “Network Science” … On the scientific community as a whole –General excitement (huge number of papers) –The Internet story has been repeated in the context of biological networks, social networks, etc. –Renewed hope that large-scale complex networks across the domains (e.g., engineering, biology, social sciences) exhibit common features (universal properties).

46. 46 On the Impact of “Network Science” … NYT 4/18/2010

47. 47 On the Impact of “Network Science” … On the scientific community as a whole –General excitement (huge number of papers) –The Internet story has been repeated in the context of biological networks, social networks, etc. –Renewed hope that large-scale complex networks across the domains (e.g., engineering, biology, social sciences) exhibit common features (universal properties). On domain experts (e.g., Internet researchers, biologists) –General disbelief –We “know” the claims are not true … –Back to basics ….

48. 48 Basic Question 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? Key Issues What about data hygiene? What about statistical rigor? What about model validation?

49. On Data Hygiene

50. 50 On Measuring Internet Connectivity No central agency/repository Economic incentive for ISPs to obscure network structure Direct inspection is typically not possible Based on measurement experiments, hacks Mismatch between what we want to measure and can measure Specific examples covered in this talk –Physical connectivity (routers, switched, links)

51. 51 Measurements: traceroute tool traceroute www.duke.edu traceroute to www.duke.edu (152.3.189.3), 30 hops max, 60 byte packets 1 fp-core.research.att.com (135.207.16.1) 2 ms 1 ms 1 ms 2 ngx19.research.att.com (135.207.1.19) 1 ms 0 ms 0 ms 3 12.106.32.1 1 ms 1 ms 1 ms 4 12.119.12.73 2 ms 2 ms 2 ms 5 tbr1.n54ny.ip.att.net (12.123.219.129) 4 ms 5 ms 3 ms 6 ggr7.n54ny.ip.att.net (12.122.88.21) 3 ms 3 ms 3 ms 7 192.205.35.98 4 ms 4 ms 8 ms 8 jfk-core-02.inet.qwest.net (205.171.30.5) 3 ms 3 ms 4 ms 9 dca-core-01.inet.qwest.net (67.14.6.201) 11 ms 11 ms 11 ms 10 dca-edge-04.inet.qwest.net (205.171.9.98) 11 ms 15 ms 11 ms 11 gw-dc-mcnc.ncren.net (63.148.128.122) 18 ms 18 ms 18 ms 12 rlgh7600-gw-to-rlgh1-gw.ncren.net (128.109.70.38) 18 ms 18 ms 18 ms 13 roti-gw-to-rlgh7600-gw.ncren.net (128.109.70.18) 20 ms 20 ms 20 ms 14 art1sp-tel1sp.netcom.duke.edu (152.3.219.118) 23 ms 20 ms 20 ms 15 webhost-lb-01.oit.duke.edu (152.3.189.3) 21 ms 38 ms 20 ms

52. 52 Traceroute measurements revisited (1) traceroute is strictly about IP-level connectivity –Originally developed by Van Jacobson (1988) –Designed to trace out the route to a host Using traceroute to map the router-level topology –Engineering hack –Example of what we can measure, not what we want to measure! Basic problem #1: IP alias resolution problem –How to map interface IP addresses to IP routers –Largely ignored or badly dealt with in the past –New efforts in 2008 for better heuristics …

53. 53 Interfaces 1 and 2 belong to the same router

54. Example: Abilene Network

55. 55 IP Alias Resolution Problem for Abilene (thanks to Adam Bender)

56. 56 IP Alias Resolution Problem for Abilene (thanks to Adam Bender)

57. 57 Node Degree Actual vs Inferred Node Degrees 0 5 10 15 20 25 01234567891011121314151617 Count actual inferred

58. 58 Traceroute measurements revisited (2) traceroute is strictly about IP-level connectivity Basic problem #2: Layer-2 technologies (e.g., MPLS, ATM) –MPLS is an example of a circuit technology that hides the network’s physical infrastructure from IP –Sending traceroutes through an opaque Layer-2 cloud results in the “discovery” of high-degree nodes, which are simply an artifact of an imperfect measurement technique. –This problem has been largely ignored in all large-scale traceroute experiments to date.

59. 59 (a)(b)

60. 60

61. 61 Traceroute measurements revisited (3) The irony of traceroute measurements –The high-degree nodes in the middle of the network that traceroute reveals are not for real … –If there are high-degree nodes in the network, they can only exist at the edge of the network where they will never be revealed by generic traceroute-based experiments … Additional sources of errors –Bias in (mathematical abstraction of) traceroute –Has been a major focus within CS/Networking literature –Non-issue in the presence of above-mentioned problems

62. 62 Traceroute measurements revisited (4) Bottom line –(Current) traceroute measurements are of little use for inferring router-level connectivity –It is unlikely that future traceroute measurements will be more useful for the purpose of router-level inference Lessons learned –Key question: Can you trust the available data? –Critical role of Data Hygiene in the Petabyte Age –Corollary: Petabytes of garbage = garbage –Data hygiene is often viewed as “dirty/unglamorous” work

63. On Model Validation

64. 64 Taking Model validation more serious … Criticism of conventional model validation –For one and the same observed phenomenon, there are usually many different explanations/models –The ability to reproduce a few graph statistics does not constitute “serious” model validation –Model validation should be more than “data fitting” What constitutes “more serious” model validation? –There is more to networks than connectivity … –When “nodes” and “links” have specific meaning … –What do real networks look like?

65. 65 Cisco 12000 Series Routers ChassisRack sizeSlots Switching Capacity 12416Full16320 Gbps 124101/210200 Gbps 124061/46120 Gbps 124041/8480 Gbps Modular in design, creating flexibility in configuration. Router capacity is constrained by the number and speed of line cards inserted in each slot. Source: www.cisco.com

66. 66 10 0 1 2 Degree 10 10 0 1 2 3 Bandwidth (Gbps) 15 x 1-port 10 GE 15 x 3-port 1 GE 15 x 4-port OC12 15 x 8-port FE Technology constraint Total Bandwidth Router Technology Constraint Cisco 12416 GSR, circa 2002 high BW low degree high degree low BW

67. 67 SOX U. Florida U. So. Florida Miss State GigaPoP WiscREN SURFNet MANLAN Northern Crossroads Mid-Atlantic Crossroads Drexel U. NCNI/MCNCMAGPI UMD NGIX Seattle Sunnyvale Los Angeles Houston Denver Kansas City Indian- apolis Atlanta Wash D.C. Chicago New York OARNET Northern Lights Indiana GigaPoP Merit U. Louisville NYSERNet U. Memphis Great Plains OneNet U. Arizona Qwest LabsCHECS-NET Oregon GigaPoP Front Range GigaPoP Texas TechTulane U. Texas GigaPoP LaNet UT Austin CENICUniNet NISN Pacific Northwest GigaPoP U. Hawaii Pacific Wave TransPAC/APAN Iowa St. Florida A&M UT-SW Med Ctr. SINet WPI Star- Light Intermountain GigaPoP Abilene Backbone Physical Connectivity (as of August 2004) 0.1-0.5 Gbps 0.5-1.0 Gbps 1.0-5.0 Gbps 5.0-10.0 Gbps DREN Jackson St. NREN USGS U. So. Miss. PSC DARPA BossNet SFGP/ AMPATH Arizona St. ESnet GEANT North Texas GigaPoP

68. 68 Cisco 750X Cisco 12008 Cisco 12410 dc1 dc2 dc3 hpr dc1 dc3 hpr dc2 dc1 dc2 hpr SAC OAK SVL LAX SDG SLO dc1 FRG dc1 FRE dc1 BAK dc1 TUS dc1 SOL dc1 COR dc1 hpr dc1 dc2 dc3 hpr OC-3 (155 Mb/s) 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) Abilene Los Angeles Abilene Sunnyvale The Corporation for Education Network Initiatives in California (CENIC) acts as ISP for the state's colleges and universities http://www.cenic.org Like Abilene, its backbone is a sparsely-connected mesh, with relatively low connectivity and minimal redundancy. no high-degree hubs? no Achilles’ heel?

69. 69

70. 70 Back to the Basic Question: 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! Longer Answer: Real-world router-level topologies look nothing like PA- type networks The results derived from PA-type models of the Internet are not “controversial” – they are simply wrong! “The tragedy of science – the slaying of a beautiful hypothesis by an ugly fact.” (T. Huxley)

71. 71 What Went Wrong? No critical assessment of available data Ignore all networking-related “details” –Randomness enters via generic attachment mechanism –Overarching desire to reproduce power law node degree distributions Low model validation standards –Reproducing observed node degree distribution

72. 72 How to avoid such Fallacies? Know your data! Take model validation more serious! Apply an engineering perspective to engineered systems!

73. 73 Internet Modeling: An Engineering Perspective Surely, the way an ISP designs its physical infrastructure is not the result of a series of coin tosses … –ISPs design their router-level topology for a purpose, namely to carry an expected traffic demand –Randomness enters in terms of uncertainty in traffic demands –ISPs are constrained in what they can afford to build, operate, and maintain (technology, economics). Decisions of ISPs are driven by objectives (performance) and reflect tradeoffs between what is feasible and what is desirable (heuristic optimization) –Constrained optimization as modeling language –Power law node degrees are a non-issue!

74. 74 Heuristically Optimized Topologies (HOT) Given realistic technology constraints on routers, how well is the network able to carry traffic? Step 1: Constrain to be feasible Abstracted Technologically Feasible Region 1 10 100 1000 10000 100000 1000000 101001000 degree Bandwidth (Mbps) Step 3: Compute max flow BiBi BjBj x ij Step 2: pick traffic demand model

75. 75 HOT Design Principles Hosts Edges Cores Mesh-like core of fast, low degree routers High degree nodes are at the edges.

76. 76 Preferential Attachment HOT model

77. 77 HOT- vs. PA-type Network Models Attack hubsHijack networkFragility FragileRobustAttack Tolerance Low throughputHigh throughputPerformance RandomDesignedGeneration Power lawHighly VariableDegree distribution CoreEdgeHigh degree nodes Slow, high degreeFast, low degreeCore nodes PA-type models HOT-type/ Internet Features

78. 78 Implications of this Engineering Perspective Important lessons learned –Know your data! – they typically reflect what we can measure rather than what we would like to measure –Avoid the allure of PA-type network models! – there exist more relevant, interesting, and rewarding network models that await discovery –Details do matter! – layers, protocols, feedback control, etc. Network resilience – more than “knocking out” nodes/links –NYC 9/11/2001, Baltimore tunnel fire (July 2001) –Eastern US/Canada blackout (August 2003) –Taiwan earthquake (December 2006) –Hijack BGP (“blackholing”, YouTube and Pakistan ISP, 2008)

79. 79 Towards an alternative “Network Science” … HOT–type network models –Very recent alternative to PA-type models Engineering view causes paradigm shift for network modeling –Network modeling ≠ exercise in data fitting –Network modeling = exercise in reverse-engineering Network resilience is a hard problem –More than “knocking out nodes”, details matter! On turning “Network Science” into a science … –Progress has been slow –“Scientists Strive to Map the Shape-Shifting Net” (NYT article 3/1/10)

80. 80 And always keep in mind … “When exactitude is elusive, it is better to be approximately right than certifiably wrong.” (B.B. Mandelbrot)

81. 81 SOME RELATED REFERENCES L. Li, D. Alderson, W. Willinger, and J. Doyle, A first-principles approach to understanding the Internet’s router-level topology, Proc. ACM SIGCOMM 2004. J.C. Doyle, D. Alderson, L. Li, S. Low, M. Roughan, S. Shalunov, R. Tanaka, and W. Willinger. The "robust yet fragile" nature of the Internet. PNAS 102(41), 2005. D. Alderson, L. Li, W. Willinger, J.C. Doyle. Understanding Internet Topology: Principles, Models, and Validation. ACM/IEEE Trans. on Networking 13(6), 2005. R. Oliveira, D. Pei, W. Willinger, B. Zhang, L. Zhang. In Search of the elusive Ground Truth: The Internet's AS-level Connectivity Structure. Proc. ACM SIGMETRICS 2008. B. Krishnamurthy and W. Willinger. What are our standards for validation of measurement-based networking research? Proc. ACM HotMetrics Workshop 2008. W. Willinger, D. Alderson, and J.C. Doyle. Mathematics and the Internet: A Source of Enormous Confusion and Great Potential. Notices of the AMS, Vol. 56, No. 2, 2009. Reprinted in: The Best Writing on Mathematics, Princeton University Press, 2010. M. Roughan, W. Willinger, O. Maennel, D. Perouli, and R. Bush. 10 Lessons from 10 years of measuring and modeling the Internet’s Autonomous Systems. IEEE JSAC Special Issue on “Measurement of Internet topologies,” 2011.