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An Introduction to  Network Theory Kyle Findlay [email_address] R&D Executive TNS Global Brand Equity Centre Presented at the SAMRA 2010 Conference Mount Grace Country House and Spa, Magaliesburg, South Africa, from 2 to 5 June 2010
What is a network? ,[object Object],[object Object]
“ A  collection  of objects  connected  to each other in some fashion” [Watts, 2002]
[object Object],[object Object],[object Object],What is a network? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Source: Six Degrees, Duncan Watts, 2002 The blogosphere Proliferation of landlines in London Human genome Quaking Aspen (one of the largest organisms in the world – these trees represent a single organism with a shared root system) Rabbit cell
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Networks used to be thought of as  fixed structures What is a network?
Shipping (sea) networks Telecommunications networks Air traffic network Data networks Source: Britain From Above ( http:// www.bbc.co.uk/britainfromabove ) CAUTION: Gratuitous network shots
Network thinking  can be applied almost  anywhere !
[object Object],[object Object],Where’s it applied? URL: http:// www.youtube.com/watch?v =PufTeIBNRJ4
[object Object],[object Object],Where’s it applied? URL: http:// www.youtube.com/watch?v =8C_dnP2fvxk
Engineering e.g. creation of robust infrastructure (e.g. electricity, telecoms), rust formation (natural growth processes similar to diffusion limited aggregation) Where’s it applied? URL: http:// www.youtube.com/watch?v =lRZ2iEHFgGo   URL: http:// www.youtube.com/watch?v = AEoP-XtJueo
Technology e.g. mapping the online world, making networks resilient in the face of cyber-terrorism, optimising cellular networks, controlling air traffic Where’s it applied? URL: http:// www.youtube.com/watch?v =l-RoDv7c5ok   URL: http:// www.youtube.com/watch?v =o4g930pm8Ms   Vid not working
Biology e.g. fish swimming in schools, ant colonies, birds flying in formation, crickets chirping in unison, giant honeybees shimmering Where’s it applied? URL: http:// www.youtube.com/watch?v =Sp8tLPDMUyg   URL: http:// www.youtube.com/watch?v =YadP3w7vkJA
Medicine e.g. cell formation, nervous system, neural networks Where’s it applied? Source: The Human Brain Book by Rita Carter
And, most interestingly…society e.g. interactions between people (e.g. Facebook; group behaviour) Where’s it applied? URL: http:// www.youtube.com/watch?v =9n9irapdON4 URL: http:// www.youtube.com/watch?v =sD2yosZ9qDw
[object Object],[object Object],[object Object],Some terminology…
[object Object],[object Object],[object Object],Important network features: Clustering co-efficient ,[object Object],[object Object],c = 0 Some nodes connected c = 1/3 ,[object Object],c = 1
[object Object],[object Object],*Source: Six Degrees, Duncan Watts, 2002 None of Ego’s friends know each other* All of Ego’s friends know each other Important network features: Clustering co-efficient
[object Object],[object Object],Source: http://flickr.com/photos/11242012@N07/1363558436   Important network features: Clustering co-efficient
[object Object],[object Object],Important network features: Average path length
[object Object],Node 10  connections or “ edges ” Important network features: Degree distribution 3 2 1 4 5 6 7 8 10 9
[object Object],*Source: Six Degrees, Duncan Watts, 2002 3 main types of networks 2  Clustering 3  Ave path length 1  Randomness ,[object Object],[object Object],[object Object],<< Level of randomness of links >> β=0 β=1
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],3 main types of networks: Grid/Lattice network Molecule 1D lattice Diamond (crystal) lattice Bismuth crystal
[object Object],[object Object],3 main types of networks: Small world network Source: http://en.wikipedia.org/wiki/Small-world_network   ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],3 main types of networks: Random network
[object Object],[object Object],[object Object],The big picture ,[object Object],[object Object]
[object Object],[object Object],And market research? How will word of my  brand  permeate  through my target market? ? How will  negative publicity  about my brand spread and be interpreted? ? Who are the  gatekeepers   in a community that most affect the  flow of information ? ? ,[object Object],[object Object],? ,[object Object],[object Object],?
[object Object],[object Object],[object Object],And market research? ,[object Object],[object Object],[object Object],[object Object]
Next: Interesting discussion points… End of main presentation
[object Object],[object Object],[object Object],Some interesting bits: A network in action Source: http://www.funny-games.biz/reaction-effect.html
[object Object],[object Object],[object Object],URL: http:// www.youtube.com/watch?v =Q77YBmtd2Rw   Some interesting bits:  How ideas spread
Some interesting bits:  How ideas spread ,[object Object],[object Object],[object Object],[object Object],[object Object],vs.
[object Object],[object Object],[object Object],Some interesting bits:  How ideas spread
[object Object],Some interesting bits: Distributed intelligence ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],Some interesting bits: Distributed intelligence
Some interesting bits: Distributed intelligence Ant colony Source: http:// www.youtube.com/watch?v =ozkBd2p2piU   URL: http:// www.youtube.com/watch?v =ozkBd2p2piU
[object Object],*Source: Six Degrees, Duncan Watts, 2002, p.89 Random re-wirings Long average path length Dramatically reduced average path length Some interesting bits: Random re-wirings “ 8” “ 3”
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],*Source: Six Degrees, Duncan Watts, 2002, p.58-61 A B C Some interesting bits: Triadic closure
*Source: Six Degrees, Duncan Watts, 2002, p.58-61 A B C ,[object Object],[object Object],[object Object],[object Object],[object Object],Some interesting bits: Triadic closure
*Source: Six Degrees, Duncan Watts, 2002, p.78-79 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Some interesting bits: Triadic closure
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Source: Wikipedia, Small world experiment Wikipedia, Six degrees of separation ,[object Object],[object Object],[object Object],Some interesting bits: Six degrees of separation
[object Object],[object Object],[object Object],*Source: Six Degrees, Duncan Watts, 2002 Some interesting bits: Six degrees of separation
Some interesting bits: Six degrees of separation What’s your Erdős number? (Scientific equivalent of The Kevin Bacon Game) “ Apocalypse” by XKCD Alt text for this comic:  &quot;I wonder if I still have time to go shoot a short film with Kevin Bacon?&quot; URL:  http://xkcd.com/599/
[object Object],[object Object],[object Object],This is what a power law distribution looks like* If you take the log of both axes, you should get a straight line* *Image source: Six Degrees, Duncan Watts, 2002 Some interesting bits: Scale-free networks  & power laws
[object Object],[object Object],[object Object],Taking the log-log of a power law distribution should show a straight line* However, in practice, the line is generally only straight for some area of the graph* *Image source: Six Degrees, Duncan Watts, 2002 Some interesting bits: Scale-free networks  & power laws
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Some interesting bits: Scale-free networks  & power laws
[object Object],[object Object]
 
 
 
[object Object],[object Object],It’s a small world after all  

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An Introduction to Network Theory

  • 1. An Introduction to Network Theory Kyle Findlay [email_address] R&D Executive TNS Global Brand Equity Centre Presented at the SAMRA 2010 Conference Mount Grace Country House and Spa, Magaliesburg, South Africa, from 2 to 5 June 2010
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  • 3. “ A collection of objects connected to each other in some fashion” [Watts, 2002]
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  • 6. Shipping (sea) networks Telecommunications networks Air traffic network Data networks Source: Britain From Above ( http:// www.bbc.co.uk/britainfromabove ) CAUTION: Gratuitous network shots
  • 7. Network thinking can be applied almost anywhere !
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  • 10. Engineering e.g. creation of robust infrastructure (e.g. electricity, telecoms), rust formation (natural growth processes similar to diffusion limited aggregation) Where’s it applied? URL: http:// www.youtube.com/watch?v =lRZ2iEHFgGo URL: http:// www.youtube.com/watch?v = AEoP-XtJueo
  • 11. Technology e.g. mapping the online world, making networks resilient in the face of cyber-terrorism, optimising cellular networks, controlling air traffic Where’s it applied? URL: http:// www.youtube.com/watch?v =l-RoDv7c5ok URL: http:// www.youtube.com/watch?v =o4g930pm8Ms Vid not working
  • 12. Biology e.g. fish swimming in schools, ant colonies, birds flying in formation, crickets chirping in unison, giant honeybees shimmering Where’s it applied? URL: http:// www.youtube.com/watch?v =Sp8tLPDMUyg URL: http:// www.youtube.com/watch?v =YadP3w7vkJA
  • 13. Medicine e.g. cell formation, nervous system, neural networks Where’s it applied? Source: The Human Brain Book by Rita Carter
  • 14. And, most interestingly…society e.g. interactions between people (e.g. Facebook; group behaviour) Where’s it applied? URL: http:// www.youtube.com/watch?v =9n9irapdON4 URL: http:// www.youtube.com/watch?v =sD2yosZ9qDw
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  • 28. Next: Interesting discussion points… End of main presentation
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  • 35. Some interesting bits: Distributed intelligence Ant colony Source: http:// www.youtube.com/watch?v =ozkBd2p2piU URL: http:// www.youtube.com/watch?v =ozkBd2p2piU
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  • 42. Some interesting bits: Six degrees of separation What’s your Erdős number? (Scientific equivalent of The Kevin Bacon Game) “ Apocalypse” by XKCD Alt text for this comic: &quot;I wonder if I still have time to go shoot a short film with Kevin Bacon?&quot; URL: http://xkcd.com/599/
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Editor's Notes

  1. New paradigm: “real networks represent populations of individual components that are actually doing something” [Watts, 2002] In other words, networks are dynamic objects that are continually changing Understanding a network is important because its structure affects the individual components’ behaviour and/or the behaviour of the system as a whole Networks are key to understanding non-linear, dynamic systems… … just like those represented by almost every facet of the universe… … from the atomic level right through to the cosmic level The important part is that the components are not acting independently – they are affected by the components around them! Note: links between component may be physical (e.g. power cable, magnetism) or conceptual (e.g. social connections)
  2. Duncan Watts and Steven Strogatz introduced the measure in 1998 Tells you how likely a node is to be connected to its neighbours… … and, importantly, how likely that its neighbours are connected to each other Put another way, it tells you how close a node and its neighbors are to being a clique where “everybody knows everyone else”
  3. Project Description: In 2006, FAS analyzed the director interlock relationships between Fortune 500 companies in California. We looked at how companies are connected through their board of directors, i.e. Apple and Disney are connected through Steve Jobs since he serves on both boards. Companies that share a lot of directors create denser zones in the network and form clusters. We measured which companies exert the largest influence overall and within each cluster. This reveals compelling new insights into key account management. Legend: The triangles represent Fortune 500 companies in CA. The larger the triangle, the more influential the company is. Companies of the same color belong to the same network cluster. If company A and company B share a director, they are linked by a line. The more directors shared, the thicker the line.