Network Science

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Network Science
Albert-László Barabási Center for Complex
Networks Research Northeastern University Departme
nt of Medicine and CCSB Harvard Medical School
www.BarabasiLab.com
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Reduces Inflammation Fever Pain
Prevents Heart attack Stroke
COX2
Reduces the risk of Alzheimer's Disease
Reduces the risk of breast cancer ovarian
cancers colorectal cancer
Causes Bleeding Ulcer
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Structure of an organization
Red, blue, or green departments Yellow
consultants Grey external
experts
www.orgnet.com
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Business ties in US biotech-industry
Nodes companies investment pharma research
labs public biotechnology

Links collaborations financial RD
http//ecclectic.ss.uci.edu/drwhite/Movie
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Erdös-Rényi model (1960)
Pál Erdös (1913-1996)
- Democratic - Random
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WWW
World Wide Web
Nodes WWW documents Links URL links
Over 10 billion documents
Exponential Network
ROBOT collects all URLs found in a document and
follows them recursively
Scale-free Network
R. Albert, H. Jeong, A-L Barabási, Nature, 401
130 (1999).
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Internet-Map
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Bacon 1
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Actors
ACTOR CONNECTIVITIES
Nodes actors Links cast jointly
Days of Thunder (1990) Far and Away (1992)
Eyes Wide Shut (1999)
N 212,250 actors ?k? 28.78
P(k) k-?
?2.3
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Coauthorship
Online communities
Pussokram.com online community 512 days, 25,000
users.
Nodes online user Links email contact
Kiel University log files 112 days, N59,912
nodes
Ebel, Mielsch, Bornholdtz, PRE 2002.
Holme, Edling, Liljeros, 2002.
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Bio-Map
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Metab-movie
Metabolic Network
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Swedish sex-web
Nodes people (Females Males) Links sexual
relationships
4781 Swedes 18-74 59 response rate.
Liljeros et al. Nature 2001
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Organizing Principles of Complex Networks

• Scale-free Many small nodes held together
  by a few hubs.
• Small World Short paths between any two nodes.
• Evolution Hubs emerge through growth and
  preferential attachment.
• Competition Nodes with high fitness become hubs.
• Robustness Resilience against random errors
  fragility to attacks (Achilles Heel).
• Communities Groups are discoverable in social
  networks

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Six Degrees (small worlds)
Sarah
Ralph
Jane
Peter
Frigyes Karinthy, 1929 Stanley Milgram, 1967
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Organizing Principles of Complex Networks

• Scale-free Many small nodes held together
  by a few hubs.
• Small World Short paths between any two nodes.
• Evolution Hubs emerge through growth and
  preferential attachment.
• Competition Nodes with high fitness become hubs.
• Robustness Resilience against random errors
  fragility to attacks (Achilles Heel).
• Communities Groups are discoverable in social
  networks

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Many real world networks have a similar
architecture
Scale-free networks
WWW, Internet (routers and domains), electronic
circuits, computer software, movie actors,
coauthorship networks, sexual web, instant
messaging, email web, citations, phone calls,
metabolic, protein interaction, protein domains,
brain function web, linguistic networks, comic
book characters, international trade, bank
system, encryption trust net, energy landscapes,
earthquakes, astrophysical network
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BA model
Origin of SF networks Growth and preferential
attachment
GROWTH add a new node with m links
PREFERENTIAL ATTACHMENT the probability that a
node connects to a node with k links is
proportional to k.
Barabási Albert, Science 286, 509 (1999)
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Organizing Principles of Complex Networks

• Scale-free Many small nodes held together
  by a few hubs.
• Small World Short paths between any two nodes.
• Evolution Hubs emerge through growth and
  preferential attachment.
• Competition Nodes with high fitness become
  hubs.
• Robustness Resilience against random errors
  fragility to attacks (Achilles
  Heel).
• Communities Groups are discoverable in social
  networks

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Fitness Model Can Latecomers Make It?
SF model k(t)t ½ (first mover
advantage)
Fitness model fitness (h )
k(h,t)tb(h) b(h) h/C
Degree (k)
time
Bianconi Barabási, Physical Review Letters
2001 Europhys. Lett. 2001.
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Organizing Principles of Complex Networks

• Scale-free Many small nodes held together
  by a few hubs.
• Small World Short paths between any two nodes.
• Evolution Hubs emerge through growth and
  preferential attachment.
• Competition Nodes with high fitness become
  hubs.
• Robustness Resilience against random errors
  fragility to attacks (Achilles Heel).
• Communities Groups are discoverable in social
  networks

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Robustness
Robustness
Complex systems maintain their basic functions
even under errors and failures
(cell ?
mutations Internet ? router breakdowns)
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Robust-SF
Robustness of scale-free networks
Attacks
Failures
? ? 3 fc1 (R. Cohen et al PRL, 2000)
fc
Albert, Jeong, Barabási, Nature 406 378 (2000)
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Organizing Principles of Complex Networks

• Scale-free Many small nodes held together
  by a few hubs.
• Small World Short paths between any two nodes.
• Evolution Hubs emerge through growth and
  preferential attachment.
• Competition Nodes with high fitness become
  hubs.
• Robustness Resilience against random errors
  fragility to attacks
  (Achilles Heel).
• Communities Groups are discoverable in social
  networks

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Zoom
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Animation
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Midnight and Noon
Noon
Midnight
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Organizing Principles of Complex Networks

• Scale-free Many small nodes held together
  by a few hubs.
• Small World Short paths between any two nodes.
• Evolution Hubs emerge through growth and
  preferential attachment.
• Competition Nodes with high fitness become hubs.
• Robustness Resilience against random errors
  fragility to attacks (Achilles
  Heel).
• Communities Groups are discoverable in social
  networks

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Spreading Processes on Networks
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A Piece of a Call Network (Mobile Phones)
weak links
strong links
community
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The strength of weak ties
Granovetter, 1973
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Diffusion of information

• Knowledge of information diffusion based on
  unweighted networks
• Does the local relationship between topology and
  tie strength have an effect?
• Spreading simulation infect one node as in
  SI-model in epidemiology
• (1) Empirical
• (2) Reference
• Spreading significantly faster on the reference
  network
• Information gets trapped in communities in the
  real network

reference
empirical
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Diffusion of information

• ? Where do individuals get their information
  from?
• Reference
• - Transmission probability independent of link
  weight
• - First transmissions through weak ties
  (Granovetter)
• Empirical
• - Transmission probability depends on link
  weight
• - First transmissions through intermediate ties
• - Weak ties ? access to new information
• ? low information transmission rate
• - Strong ties ? high information transmission
  rate
• ? rarely access to new information
• ? weakness of weak and strong ties

reference
empirical
J.P. Onella et al, PNAS 2007
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What is network science? An attempt to
understand networks emerging in nature,
technology and society using a unified set of
tools and principles. What is new here? Despite
the apparent differences, many networks emerge
and evolve driven by a fundamental set of laws
and mechanism.
 
 
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Bacon-list
Bonus Why Kevin Bacon?
Measure the average distance between Kevin Bacon
and all other actors.
No. of movies 46 No. of actors 1811
Average separation 2.79
Kevin Bacon
Is Kevin Bacon the most connected actor?
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Bacon-map
Rod Steiger
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Donald Pleasence
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Martin Sheen
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Http//www.nd.edu/networks
Réka Albert, Penn State Hawoong Jeong, KAIST,
Korea Ginestra Bianconi, ICTP, Trieste Kwang-Il
Goh, Korea University Cesar Hidalgo, Notre
Dame Mark Vidal, Dana-Farber,
Harvard Michael E. Cusick, Dana Farber,
Harvard David Valle, Johns Hopkins Barton
Childs, Johns Hopkins Nicholas Christakis,
Harvard Deok-Sun Lee, Northeastern University
DF Juyong Park, Northeastern University
DF Zoltan N. Oltvai, Pitssburgh Medical
School Dashun Wang, Northeastern
University
www.BarabasiLab.com