Title

1. Title 네트워크의 과학, 복잡한세상을 바라보는 새로운 시각 정하웅 KAIST, 물리학과 Albert László Barabási, Réka Albert (Univ. of Notre Dame) Zoltán N. Oltvai (Northwestern Univ.) www.nd.edu/~networks

2. Bacon 1 Austin Powers: The spy who shagged me Let’s make it legal Robert Wagner Wild Things What Price Glory Barry Norton A Few Good Man Monsieur Verdoux

3. Complexity Main Entry: 1com·plexFunction: nounEtymology: Late Latin complexus totality, from Latin, embrace, from complectiDate: 16431:a whole made up of complicated or interrelated parts A popular paradigm: Simple systems display complex behavior  non-linear systems  chaos  fractals 3 Body Problem Earth( ) Jupiter ( ) Sun ( ) What is Complexity?

4. Human body : chemical network NETWORKS! Society Internet

5. Society Nodes: individuals Links: social relationship (family/work/friendship/etc.) S. Milgram (1967) “Six Degrees of Separation” John Guare Social networks: Many individuals with diversesocial interactions between them.

6. 9-11 Terror Hijacker’s Network

8. Communication networks The Earth is developing an electronic nervous system, a network with diverse nodes and links are -computers -routers -satellites -phone lines -TV cables -EM waves Communication networks: Many non-identical components with diverseconnections between them.

9. GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

10. Complex systems Made of many non-identical elements connected by diverse interactions. NETWORK

11. Connect with probability p p=1/6 N=10 k ~ 1.5 Poisson distribution - Random - Democratic Erdös-Rényi model(1960) Pál Erdös(1913-1996) Degree DistributionP(k) : prob. that a certain node will have k links

12. NO! ARE COMPLEX NETWORKS REALLY RANDOM? To test this: We need to pragmatically investigate the topology of large real networks.

13. WWW ROBOT:collects all URL’s found in a document and follows them recursively World Wide Web Nodes: WWW documents Links: URL links 800 million documents (S. Lawrence, Nature,1999) R. Albert, H. Jeong, A-L Barabasi, Nature, 401 130 (1999)

14. WWW-power What did we expect? k ~ 6 P(k=500) ~ 10-99 NWWW ~ 109  N(k=500)~10-90 We find: out= 2.45 in = 2.1 P(k=500) ~ 10-6 NWWW ~ 109  N(k=500) ~ 103 Pout(k) ~ k-out Pin(k) ~ k- in J. Kleinberg, et. al, Proceedings of the ICCC (1999)

15. What does it mean? Airlines Poisson distribution Power-law distribution Exponential Network Scale-free Network

16. Internet INTERNET BACKBONE Nodes: computers, routers Links: physical lines (Faloutsos, Faloutsos and Faloutsos, 1999)

17. Internet-Map

18. SEX-Web Nodes: people (females; males) Links: sexual relationships 4781 Swedes; 18-74; 59% response rate. (Liljeros et al. Nature 2001)

19. Actors ACTOR CONNECTIVITIES Nodes: actors Links: cast jointly Days of Thunder (1990) Far and Away (1992) Eyes Wide Shut (1999) N = 212,250 actors k = 28.78 P(k) ~k- =2.3

20. Citation SCIENCE CITATION INDEX 14 Nodes: papers Links: citations D.C. Hong et al Safeman-Taylor prob. Phys. Rev. Lett. (1986) 1736 PRL papers (1988) 143 P(k) ~k- ( = 3) (S. Redner, 1998)

21. Econo network Nodes: individual, company, country... Links: economic activities Pi(t) : stock price at time t ,

22. Bio-Map GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

23. protein-protein network (yeast) p53 network (mammals) metabolic network (E. coli) Jeong et al. Nature 411, 41 (2001) Jeong et al. Nature 407, 651 (2000).

24. Other Examples of Scale-Free Network Email network Nodes: individual email address Links: email communication Phone-call networks Nodes: phone-number Links: completed phone call (Abello et al, 1999) Networks in linguistics Nodes: words Links: appear next or one word apart from each other (Ferrer et al, 2001) Networks in Electronic auction (eBay) Nodes: agents, individuals Links: bids for the same item (H. Jeong et al, 2001)

25. Most real world networks have the same internal structure: Scale-free networks How? Why?

26. Origins SF (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 ORIGIN OF 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

27. BA model 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)

28. MFT Continuum Theory , with initial condition γ = 3 A.-L.Barabási, R. Albert and H. Jeong, Physica A 272, 173 (1999)

29. Most real world networks have the same internal structure: Scale-free networks How? Why?

30. Efficiency of resource usage With same number of nodes and links (same amount of resources), construct scale-free and exponential networks. Diameter (Scale-free) < Diameter (Exponential) (Diameter : average distance between two nodes) Scale-free network is more efficient than exponential network!

31. Robustness 1 Relative size of largest cluster S fc 0 1 Fraction of removed nodes, f node failure Robustness Complex systems maintain their basic functions even under errors and failures (cell  mutations; Internet  router breakdowns)

32. Robust-SF Extreme failure tolerance Failures Topological error tolerance   3 :fc=1 (R. Cohen et al PRL, 2000) fc fc Low survivability under attacks! Attacks Robustness of scale-free networks 1 S 0 f 1

33. Achilles Heel Achilles’ Heel of complex network failure attack Internet Protein network R. Albert, H. Jeong, A.L. Barabasi, Nature 406 378 (2000)

34. Bio-informatics vs. Networks Human Genome Project completed!  Inventory of all genes  Only list of proteins Post Genome Era • Transcriptomics • Proteomics Needs information on interactions “Human Network Project”

35. GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

36. METABOLISM Bio-chemical reactions Citrate Cycle

37. Boehring-Mennheim

38. Nodes: chemicals (proteins, substrates) Links: bio-chem. reaction Metabolic Networks

39. Metabolic networks Archaea Bacteria Eukaryotes Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000)

40. Properties of metabolic networks Average distances are independent of organisms!  by making more links between nodes. based on “design principles” of the cellthrough evolution. cf. Other scale-free network: D~log(N)

41. GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

42. PROTEOME protein-protein interactions

43. Prot Interaction map Yeast protein network Nodes: proteins Links: physical interactions (binding) P. Uetz, et al.Nature403, 623-7 (2000).

44. Prot P(k) Topology of the protein network Power-law with exponential cut-off : (physical limitation) H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature, 411, 41 (2001)

45. [3280 protein with 4434 interactions] Japan protein data p(k) P(k) ~ k- Uetz  2.4 Ito  2.3 www.nd.edu/~networks/cell While there is only 13% overlap between the Uetz et al and Ito et al data, their large-scale topology is identical. Ito et al, PNAS 97, 1143 (2000); PNAS 98, 4569 (2001).

46. Prot- robustness Yeast protein network - lethality and topological position - Highly connected proteins are more essential (lethal) than less connected proteins.

47. GENOME protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle

48. protein-gene interactions

49. P53 Nature 408 307 (2000) “… since 1989 … there have been over 17,000 publications centered on p53 … this work has led to considerable confusion and controversy.” … “One way to understand the p53 network is to compare it to the Internet. The cell, like the Internet, appears to be a ‘scale-free network’.”

50. P53 P(k) p53 network (mammals)