Lecture 2: Introduction

1. Lecture 2: Introduction CS 765: Complex Networks Slides are modified from Statistical physics of complex networks by Sergei Maslov and Complex Adaptive Systems by Eileen Kraemer

2. Basic definitions • Network: (net + work, 1500’s) • Noun: • Any interconnected group or system • Multiple computers and other devices connected together to share information • Verb: • To interact socially for the purpose of getting connections or personal advancement • To connect two or more computers or other computerized devices slides from Peter Dodds

3. Basic definitions • Nodes = A collection of entities which have properties that are somehow related to each other • e.g., people, forks in rivers, proteins, webpages, organisms,... • Links = Connections between nodes • may be real and fixed (rivers), • real and dynamic (airline routes), • abstract with physical impact (hyperlinks), • purely abstract (semantic connections between concepts). • Links may be directed or undirected. • Links may be binary or weighted.

4. Basic definitions • Complex: (Latin = with + fold/weave (com + plex)) • Adjective • Made up of multiple parts; intricate or detailed. • Not simple or straightforward • Complex System—Basic ingredients: • Relationships are nonlinear • Relationships contain feedback loops • Complex systems are open (out of equilibrium) • Modular (nested)/multiscale structure • Opaque boundaries • May result in emergent phenomena • Many complex systems can be regarded as complex networks of physical or abstract interactions • Opens door to mathematical and numerical analysis

5. What passes for a complex network? • Complex networks are large (in node number) • Complex networks are sparse (low edge to node ratio) • Complex networks are usually dynamic and evolving • Complex networks can be social, economic, natural, informational, abstract, ... • Isn’t this graph theory? • Yes, but emphasis is on data and mechanistic explanations...

6. What is a Network? Network is a mathematical structure composed of points connected by lines Network Theory<-> Graph Theory Network  Graph Nodes  Vertices (points) Links  Edges (Lines) A network can be build for any functional system System vs. Parts = Networks vs. Nodes

7.  1 2 3 4 5 6 2.5 12.7 7.3 3.3 5.4 8.1 2.5 Vertex-Weighted Edge-Weighted Networks As Graphs • Networks can be undirected or directed, depending on whether • the interaction between two neighboring nodes proceeds in both • directions or in only one of them, respectively. • The specificity of network nodes and links can be quantitatively • characterized by weights

8. A network can be connected (presented by a single component) or • disconnected (presented by several disjoint components). connected disconnected trees cyclic graphs Networks As Graphs - 2 • Networks having no cycles are termed trees. The more cycles the • network has, the more complex it is.

9. Paths Stars Cycles Complete Graphs Bipartite Graphs Networks As Graphs - 3 Some Basic Types of Graphs

10. Historical perspective on Complex Networks • In the beginning.. there was REDUCTIONISM • All we need to know is the behavior of the system elements • Particles in physics, molecules or proteins in biology, communication links in the Internet • Complex systems are nothing but the result of many interactions between the system’s elements • No new phenomena will emerge when we consider the entire system • A centuries-old very flawed scientific tradition.. slides by Constantine Dovrolis

11. Historical perspective • During the 80’s and early 90’s, several parallel approaches departed from reductionism • Consider the entire SYSTEM attempting to understand/ explain its COMPLEXITY • B. Mandelbrot and others: Chaos and non-linear dynamical systems (the math of complexity) • P. Bak: Self-Organized Criticality – The edge of chaos • S. Wolfram: Cellular Automata • S. Kauffman: Random Boolean Networks • I. Prigogine: Dissipative Structures • J. Holland: Emergence • H. Maturana, F. Varela: Autopoiesis networks & cognition • Systems Biology

12. Historical perspective • Systems approach: thinking about Networks • The focus moves from the elements (network nodes) to their interactions (network links) • To a certain degree, the structural details of each element become less important than the network of interactions • Some system properties, such as Robustness, Fragility, Modularity, Hierarchy, Evolvability, Redundancy (and others) can be better understood through the Networks approach • Some milestones: • 1998: Small-World Networks (D.Watts and S.Strogatz) • 1999: Scale-Free Networks (R.Albert & A.L.Barabasi) • 2002: Network Motifs (U.Alon)

13. The evolution of the meaning of protein function traditional view post-genomic view from Eisenberg et al. Nature 2000 405: 823-6

14. Networks in complex systems • Complex systems • Large numberof components interacting with each other • All components and/or interactions are different from each other • Paradigms: • 104 types of proteins in an organism, • 106 routers in the Internet • 109 web pages in the WWW • 1011 neurons in a human brain • The simplest property: • who interacts with whom? • can be visualized as a network • Complex networks are just a backbone for complex dynamical systems

15. Why study the topology of Complex Networks? • Lots of easily available data • Large networks may contain information about basic design principles and/or evolutionary history of the complex system • This is similar to paleontology: • learning about an animal from its backbone

16. Early social network analysis • 1933 Moreno displays first sociogram at meeting of the Medical Society of the state of New York • article in NYT • interests: effect of networks on e.g. disease propagation • Preceded by studies of (pre)school children in the 1920’s Source: The New York Times (April 3, 1933, page 17).

17. Social Networks • Links denote a social interaction • Networks of acquaintances • collaboration networks • actor networks • co-authorship networks • director networks • phone-call networks • e-mail networks • IM networks • Bluetooth networks • sexual networks • home page/blog networks

18. Network of actor co-starring in movies

19. Actors

20. Networks of scientists’ co-authorship of papers

21. Scientists

22. boards of directors Source: http://theyrule.net

23. Political/Financial Networks • Mark Lombardi: tracked and mapped global financial fiascos in the 1980s and 1990s • searched public sources such as news articles • drew networks by hand (some drawings as wide as 10ft)

24. Understanding through visualization • “I happened to be in the Drawing Center when the Lombardi show was being installed and several consultants to the Department of Homeland Security came in to take a look. They said they found the work revelatory, not because the financial and political connections he mapped were new to them, but because Lombardi showed them an elegant way to array disparate information and make sense of things, which they thought might be useful to their security efforts. I didn't know whether to find that response comforting or alarming, but I saw exactly what they meant.” Michael KimmelmanWebs Connecting the Power Brokers, the Money and the WorldNY Times November 14, 2003

25. terrorist networks “Six degrees of Mohammed Atta”Uncloaking Terrorist Networks, by Valdis Krebs

26. Knowledge (Information) Networks • Nodes store information, links associate information • Citation network (directed acyclic) • The Web (directed) • Peer-to-Peer networks • Word networks • Networks of Trust • Software graphs

27. natural language processing • Wordnet Source: http://wordnet.princeton.edu/man/wnlicens.7WN

28. online social networks • Friendster

29. World Wide Web

30. Networks of personal homepages Stanford MIT Source: Lada A. Adamic and Eytan Adar, ‘Friends and neighbors on the web’, Social Networks, 25(3):211-230, July 2003

31. European University Web Pages

32. HP e-mail communication

33. Links among blogs (2004 presidential election)

34. Product recommendations

35. Technological networks • Networks built for distribution of commodity • The Internet • router level, AS level • Power Grids • Airline networks • Telephone networks • Transportation Networks • roads, railways, pedestrian traffic

36. The Internet at AS level

37. ASes

38. Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.

39. Routers

40. Power networks

41. transportation networks: airlines Source: Northwest Airlines WorldTraveler Magazine

42. transportation networks: railway maps Source: TRTA, March 2003 - Tokyo rail map

43. Biological networks • Biological systems represented as networks • Protein-Protein Interaction Networks • Gene regulation networks • Gene co-expression networks • Metabolic pathways • The Food Web • Neural Networks

44. metabolic networks • Citric acid cycle • Metabolites participate in chemical reactions

45. Biochemical pathways (Roche) Source: Roche Applied Science, http://www.expasy.org/cgi-bin/show_thumbnails.pl

46. gene regulatory networks • humans have 30,000 genes • the complexity is in the interaction of genes • can we predict what result of the inhibition of one gene will be? Source: http://www.zaik.uni-koeln.de/bioinformatik/regulatorynets.html.en

47. Images from ResNet3.0 by Ariadne Genomics Inhibition of apoptosis MAPK signaling

48. Bio map by L-A Barabasi protein-gene interactions PROTEOME protein-protein interactions METABOLISM Bio-chemical reactions Citrate Cycle GENOME _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - -

49. Protein binding networks Baker’s yeast S. cerevisiae(only nuclear proteins shown) Nematode worm C. elegans

50. Transcription regulatory networks Single-celled eukaryote:S. cerevisiae Bacterium:E. coli