Lecture 1:
Introduction
CS 790g: Complex Networks
Slides are modified from Statistical physics of complex networks by Sergei Maslov
and Complex Adaptive Systems by Eileen Kraemer
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
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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.
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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
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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...
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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
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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
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 The specificity of network nodes and links can be quantitatively
characterized by weights
2.5
7.3
3.3
12.7
5.4
8.1
2.5
Vertex-Weighted
Edge-Weighted
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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
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Networks As Graphs - 3
Some Basic Types of Graphs
Paths
Stars
Cycles
Complete Graphs
Bipartite Graphs
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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
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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

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



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(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
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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)
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The evolution of the meaning of protein function
traditional view
post-genomic view
from Eisenberg et al. Nature 2000 405: 823-6
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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
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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
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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).
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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
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Network of actor co-starring in movies
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Actors
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Networks of scientists’ co-authorship of papers
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Scientists
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boards of directors
Source: http://theyrule.net
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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)
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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
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terrorist networks
“Six degrees of
Mohammed Atta”
Uncloaking
Terrorist
Networks, by
Valdis Krebs
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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
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natural language processing
 Wordnet
Source: http://wordnet.princeton.edu/man/wnlicens.7WN
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online social networks
 Friendster
"Vizster: Visualizing Online Social
Networks." Jeffrey Heer and danah
boyd. IEEE Symposium on
Information Visualization (InfoViz
2005).
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World Wide Web
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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
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European University Web Pages
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HP e-mail communication
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Links among blogs (2004 presidential election)
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Product recommendations
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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
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The Internet at AS level
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Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.
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routers
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Power networks
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transportation networks: airlines
Source: Northwest Airlines WorldTraveler Magazine
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transportation networks: railway maps
Source: TRTA, March 2003 - Tokyo rail map
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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
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metabolic networks
 Citric acid cycle
 Metabolites
participate in
chemical reactions
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Biochemical pathways (Roche)
Source: Roche Applied Science, http://www.expasy.org/cgi-bin/show_thumbnails.pl
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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
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Images from ResNet3.0 by Ariadne Genomics
Inhibition of apoptosis
MAPK signaling
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Bio map by L-A Barabasi
GENOME
_____________________
-
protein-gene
interactions
-
PROTEOME
protein-protein
interactions
METABOLISM
Bio-chemical
reactions
Citrate Cycle
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Protein binding networks
Baker’s yeast S. cerevisiae
(only nuclear proteins shown)
Nematode worm C. elegans
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Transcription regulatory networks
Bacterium: E. coli
Single-celled eukaryote:
S. cerevisiae
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The Protein Network of Drosophila
CuraGen Corporation
Science, 2003
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Metabolic networks
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KEGG database: http://www.genome.ad.jp/kegg/kegg2.html
C. elegans neurons
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Network of Interacting Pathways (NIP)
381 organisms
A.Mazurie
D.Bonchev
G.A. Buck,
2007
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Freshwater food web by Neo Martinez and Richard Williams
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Examples of complex networks:
geometric, regular
slides from Eileen Kraemer
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Examples of complex networks:
semi-geometric, irregular
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Elementary features:
node diversity and dynamics
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Elementary features:
edge diversity and dynamics
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Network Questions: Structural
1.
How many connections does the average node have?
2.
Are some nodes more connected than others?
3.
Is the entire network connected?
4.
On average, how many links are there between nodes?
5.
Are there clusters or groupings within which the connections are
particularly strong?
6.
What is the best way to characterize a complex network?
7.
How can we tell if two networks are “different”?
8.
Are there useful ways of classifying or categorizing networks?
slides from David P. Feldman
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Network Questions: Communities
1. Are there clusters or groupings within which the
connections are particularly strong?
2. What is the best way to discover communities,
especially in large networks?
3. How can we tell if these communities are statistically
significant?
4. What do these clusters tell us in specific applications?
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Network Questions: Dynamics of
1. How can we model the growth of networks?
2. What are the important features of networks that our
models should capture?
3. Are there “universal” models of network growth? What
details matter and what details don’t?
4. To what extent are these models appropriate null
models for statistical inference?
5. What’s the deal with power laws, anyway?
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Network Questions: Dynamics on
1. How do diseases/computer viruses/innovations/
rumors/revolutions propagate on networks?
2. What properties of networks are relevant to the answer
of the above question?
3. If you wanted to prevent (or encourage) spread of
something on a network, what should you do?
4. What types of networks are robust to random attack or
failure?
5. What types of networks are robust to directed attack?
6. How are dynamics of and dynamics on coupled?
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Network Questions: Algorithms
1. What types of networks are searchable or navigable?
2. What are good ways to visualize complex networks?
3. How does google page rank work?
4. If the internet were to double in size, would it still work?
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Network Questions: Algorithms
There are also many domain-specific questions:
1. Are networks a sensible way to think about gene
regulation or protein interactions or food webs?
2. What can social networks tell us about how people
interact and form communities and make friends and
enemies?
3. Lots and lots of other theoretical and methodological
questions...
4. What else can be viewed as a network? Many
applications await.
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Network Questions: Outlook
 Advances in available data, computing speed, and
algorithms have made it possible to apply network
analysis to a vast and growing number of phenomena.

This means that there is lots of exciting, novel work being done.

This work is a mixture of awesome, exploratory, misleading,
irrelevant, relevant, fascinating, ground-breaking, important,
and just plain wrong.
 It is relatively easy to fool oneself into seeing thing that
aren’t there when analyzing networks.

This is the case with almost anything, not just networks.
 For networks, how can we be more careful and
scientific, and not just descriptive and empirical?
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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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