Lecture 2:

Introduction

CS 765: Complex Networks

Slides are modified from Statistical physics of complex networks by Sergei Maslovand 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 Dodds2

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.

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

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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

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Networks As Graphs - 3Some Basic Types of Graphs

Paths

Stars

Cycles

Complete Graphs

Bipartite Graphs9

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 10

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

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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

post-genomic view traditional view

from Eisenberg et al. Nature 2000 405: 823-613

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.net22

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 KimmelmanWebs Connecting the Power Brokers, the Money and the WorldNY Times November 14, 2003

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“Six degrees of Mohammed Atta”

Uncloaking Terrorist

Networks, by Valdis Krebs

terrorist networks

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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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ASes

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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 41

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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Citric acid cycle

Metabolites participate in chemical reactions

metabolic networks

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Biochemical pathways (Roche)

Source: Roche Applied Science, http://www.expasy.org/cgi-bin/show_thumbnails.pl45

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.en46

MAPK signalingInhibition of apoptosis

Images from ResNet3.0 by Ariadne Genomics

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protein-gene interactions

protein-protein interactions

PROTEOME

GENOME

Citrate Cycle

METABOLISM

Bio-chemical reactions

Bio map by L-A Barabasi

- -

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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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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KEGG database: http://www.genome.ad.jp/kegg/kegg2.html

Metabolic networks

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C. elegans neurons

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Network of Interacting Pathways (NIP)

A.Mazurie D.Bonchev G.A. Buck, 2007

381 organisms

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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 56

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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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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