lecture 2: introduction cs 765: complex networks slides are adapted from constantine dovrolis,...
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Lecture 2:
Introduction
CS 765: Complex Networks
Slides are adapted from
Constantine Dovrolis, Eileen Kraemer, Peter Dodds, and Sergei Maslov
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
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.
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
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...
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
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
2.5
2.5
7.3 3.3 12.7
8.1
5.4
Vertex-Weighted Edge-Weighted
1 2 3 4 5 6
Networks As Graphs - 2
Networks having no cycles are termed trees. The more cycles the
network has, the more complex it is.
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 - 3Some Basic Types of Graphs
Paths
Stars
Cycles
Complete Graphs
Bipartite Graphs
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..
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
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)
The evolution of the meaning of protein function
post-genomic view traditional view
from Eisenberg et al. Nature 2000 405: 823-6
Networks in complex systems
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
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
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).
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
online social networks
Friendster
"Vizster: Visualizing Online Social Networks." Jeffrey Heer and danah boyd. IEEE Symposium on Information Visualization (InfoViz 2005).
Network of actor co-starring in movies
Actors
Networks of scientists’ co-authorship of papers
Scientists
boards of directors
Source: http://theyrule.net
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)
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
“Six degrees of Mohammed Atta”
Uncloaking Terrorist
Networks, by Valdis Krebs
terrorist networks
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
natural language processing
Wordnet
Source: http://wordnet.princeton.edu/man/wnlicens.7WN
World Wide Web
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
European University Web Pages
HP e-mail communication
Links among blogs (2004 presidential election)
Product recommendations
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
The Internet at AS level
Ases
by David Shelley
Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.
Routers
Power networks
transportation networks: airlines
Source: Northwest Airlines WorldTraveler Magazine
transportation networks: railway maps
Source: TRTA, March 2003 - Tokyo rail map
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
Citric acid cycle
Metabolites participate in chemical reactions
metabolic networks
Biochemical pathways (Roche)
Source: Roche Applied Science, http://www.expasy.org/cgi-bin/show_thumbnails.pl
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
MAPK signalingInhibition of apoptosis
Images from ResNet3.0 by Ariadne Genomics
protein-gene interactions
protein-protein interactions
PROTEOME
GENOME
Citrate Cycle
METABOLISM
Bio-chemical reactions
Bio map by L-A Barabasi
- -
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Protein binding networks
Baker’s yeast S. cerevisiae (only nuclear proteins shown)
Nematode worm C. elegans
Transcription regulatory networks
Bacterium: E. coli Single-celled eukaryote: S. cerevisiae
The Protein Network of Drosophila
CuraGen Corporation Science, 2003
KEGG database: http://www.genome.ad.jp/kegg/kegg2.html
Metabolic networks
C. elegans neurons
Network of Interacting Pathways (NIP)
A.Mazurie D.Bonchev G.A. Buck, 2007
381 organisms
Freshwater food web by Neo Martinez and Richard Williams
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
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