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

3. 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 diverse connections between them.

4. New York Times Complex systems Made of many non-identical elements connected by diverse interactions . NETWORK

10. Zipf’s Law Linear scales on both axes Logarithmic scales on both axes The same data plotted on linear and logarithmic scales. Both plots show a Zipf distribution with 300 datapoints

14. Clustering : My friends will likely know each other! Probability to be connected C » p C = # of links between 1,2,…n neighbors n(n-1)/2 Networks are clustered [large C(p)] but have a small characteristic path length [small L(p)]. The Clustering Coefficient of a Network

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

21. Citrate Cycle METABOLISM Bio-chemical reactions Metabolic Network

22. Boehring-Mennheim

23. Metab-movie Nodes : chemicals (substrates) Links : bio-chemical reactions Metabolic Network

24. Meta-P(k) 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) Archaea Bacteria Eukaryotes Metabolic Network

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

26. Protein Network protein-protein interactions PROTEOME

27. Prot Interaction map Nodes : proteins Links : physical interactions (binding) P. Uetz, et al. Nature 403 , 623-7 (2000). Yeast Protein Network

28. Prot P(k) H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001) Topology of the Protein Network

29. P53 … “ 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 ’.” p53 Network Nature 408 307 (2000)

30. P53 P(k) p53 Network (mammals)