1. and Complex Adaptive Systems by Eileen Kraemer
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. Network: (net + work, 1500’s) Noun:
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. Links = Connections between nodes
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. Complex: (Latin = with + fold/weave (com + plex)) Adjective
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. 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. 1 2 3 4 5 6 
The specificity of network nodes and links can be quantitatively
characterized by weights
2.5
7.3
3.3
12.7
8.1
5.4
Vertex-Weighted
Edge-Weighted

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

9. Networks As Graphs - 3 Some Basic Types of Graphs Paths Stars Cycles
Complete Graphs
Bipartite 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 : 823-6

14. Networks in complex systems
Large number of 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. Links denote a social interaction
Social Networks
Links denote a social interaction
Networks of acquaintances
collaboration networks
actor networks
co-authorship networks
director networks
phone-call networks
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:

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 Kimmelman Webs Connecting the Power Brokers, the Money and the World NY 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:

28. online social networks
Friendster
"Vizster: Visualizing Online Social Networks." Jeffrey Heer and danah boyd. IEEE Symposium on Information Visualization (InfoViz 2005).

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): , 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 Tokyo rail map

43. Biological systems represented as networks
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,

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:

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

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

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

51. The Protein Network of Drosophila
CuraGen Corporation
Science, 2003

52. Metabolic networks
KEGG database:

53. C. elegans neurons

54. Network of Interacting Pathways (NIP)
381 organisms
A.Mazurie
D.Bonchev
G.A. Buck,
2007

55. Freshwater food web by Neo Martinez and Richard Williams

56. Examples of complex networks: geometric, regular
slides from Eileen Kraemer

57. Examples of complex networks: semi-geometric, irregular

58. Elementary features: node diversity and dynamics

59. Elementary features: edge diversity and dynamics

60. Wrap up
networks are everywhere and can be used to describe many, many systems
by modeling networks we can start to understand their properties and the implications those properties have for processes occurring on the network