From a linear world…

1. Cartography of complex networks:From organizationsto the metabolismRoger GuimeràDepartment of Chemical and Biological EngineeringNorthwestern UniversityOxford, June 19, 2006

2. From a linear world… Predator Predator Predator Consumer Consumer Consumer Consumer Resource Resource Resource Resource Resource Food “tree” Food chains

3. …to the real world The Biosphere2 project

4. Trophic interactions in the North Atlantic fishery: a real food web

5. The email network of a real organization Guimera, Danon, Díaz-Guilera, Giralt, Arenas, PRE (2002)

6. The worldwide air transportation network: a real socio-economic network Guimera, Mossa, Turtschi, Amaral, PNAS (2005)

7. The protein interactome of yeast: a real biochemical network Jeong, Mason, Barabasi, Oltvai, Nature (2001)

8. Summary • What is (was) missing in the analysis of complex systems? • Cartography of complex networks: • Modules in complex networks • Roles in complex networks • Can we discover new therapeutic drugs by analyzing complex networks?

9. Let’s assume that... ...proteins/people interact at random with other proteins/people

10. Let’s assume that... ...individuals live in a square lattice!!

11. Nodes in real networks are (often) “close” to each other

12. Nodes in real networks (often) have structured neighborhoods

13. Real networks are (often) highly inhomogeneous

14. Real networks are (often) modular

15. What can we learn by studying the interaction network topology?

16. Extracting information from complex networks Protein interactions in fruit fly Giot et al., Science (2003)

17. We need a “cartography” of complex networks • Modules One divides the system into “regions” • Roles One highlights important players

18. Heuristic methods to identify modules in complex networks: Girvan-Newman algorithm A • Identify the most central edge in the network B D • Remove the most central edge in the network C E • Iterate the process F G H I Girvan & Newman, PNAS (2002)

19. The Girvan-Newman algorithm for module detection is remarkably effective

20. The community tree of a real organization

21. Shortcomings of the GN algorithm • It is very slow: O(N3) • One needs to decide where to stop the process • It does not work that well when the modular structure becomes fuzzy

22. We define a quantitative measure of modularity High modularity Low modularity Intuitively high modularity = many links within & few links between Newman & Girvan, PRE (2003)

23. We define a quantitative measure of modularity Fs: expected fraction of links within module s,for a random partition of the nodes Modularity of a partition: M = (fs – Fs) fs: fraction of links within module s Newman & Girvan, PRE (2003); Guimera, Sales-Pardo, Amaral, PRE (2004)

24. But now that we have modularity, we can try optimization-based approaches • Brute force: Find all possible partitions of the network, calculate their modularity, and keep the partition with the highest modularity. • Uphill search: • Start from a random partition of the network. • Try to randomly move a node from one module to another. Does the modularity increase? • Yes: Accept the movement. • No: Reject the movement. • Repeat from 2

25. Uphill search does not give the best possible partition

26. We use simulated annealing to obtain the partition with largest modularity • Simulated annealing: • Start from a random partition of the network. • Define a “computational temperature” T. Set T to a high value. • Try to randomly move a node from one module to another. Does the modularity increase? • Yes: Accept the movement. • No: Is the decrease in modularity much larger than T? • Yes: Reject the movement. • No: Sometimes accept the movement. • Decrease T and repeat from 3. Guimera & Amaral, Nature (2005)

27. We use simulated annealing to obtain the partition with largest modularity Simulated Annealing

28. The new algorithm for module detection outperforms previous algorithms

29. As we already knew, geo-political factors determine the modular structure of the air transportation network Guimera, Mossa Turtschi, Amaral, PNAS (2005)

30. Now we need to identify the role of each node

31. Previous approaches to role identification:Structural equivalence Definition Two nodes are structurally equivalent if, for all actors, k=1, 2, …, g (k=i, j), and all relations r =1, 2, …, R, actor i has a tie to k, if and only if j also has a tie to k, and i has a tie from k if and only if j also has a tie from k. (Wasserman & Faust) ‘Translation’ Two nodes are structurally equivalent if they have the exact same connections.

32. Previous approaches to role identification:Regular equivalence Definition If actors i and j are regularly equivalent, and actor i has a tie to/from some actor, k, then actor j must have the same kind of tie to/from some actor, m, and k and m must be regularly equivalent. (Wasserman & Faust) ‘Translation’ Two nodes are regularly equivalent if they have identical connections to equivalent nodes.

33. We define the within-module degree Within-module relative degree where: • k i: number of links of node iinside its own module

34. We define the participation coefficient Participation coefficient where: • fis: fraction of links of node i in module s

35. The within-module degree and the participation coefficient define the role of each node

36. We define seven different roles Global hub Hubs Provincial hub Non-hubs Peripheral Satellite connector Ultra-peripheral

37. Our definition of roles enables us to identify important cities

38. How does network cartography help us understand the metabolism? Metabolic network of E. coli

39. The cartographic representation of the metabolic network of E. coli Satellite Global Guimera & Amaral, Nature (2005)

40. Satellite connectors are more conserved across species than provincial hubs • Comparison between 12 organisms: • 4 archea • 4 bacteria • 4 eukaryotes Ultra-peripheral Peripheral Satellite connectors Provincial hubs Global hubs

41. Fluxes involving satellite connectors are essential Guimera, Sales-Pardo, Amaral, submitted (2006)

42. Questions for us to think • Can we design better organizations / transportation systems / … by using these new tools? • What can we learn from organizations / … that could help us design better drugs? • How are topology, dynamics, and function related?

43. Acknowledgements • Luís A. N. Amaral, Marta Sales-Pardo • Fulbright Commission and Spanish Ministry of Education, Culture, and Sports. More information: http://amaral.northwestern.edu/ http://amaral.northwestern.edu/roger/

44. What happens if the modular structure of the network is hierarchically organized?

45. To determine the hierarchical modular structure of the network, we sample the whole modularity landscape Sales-Pardo, Guimera, Moreira, Amaral, submitted (2006)

46. We are able to identify the modules at each of the hierarchical levels Nodes Nodes Sales-Pardo, Guimera, Moreira, Amaral, submitted (2006)

47. We are able to identify the modules at each of the hierarchical levels Sales-Pardo, Guimera, Moreira, Amaral, submitted (2006)