An Introduction to Network Theory
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The document discusses networks and network theory. It defines what a network is and provides examples of networks in nature, society, and technology. It also discusses key network concepts like nodes, edges, average path length, clustering coefficients, and different types of networks including random, lattice, and small-world networks. Power laws and scale-free networks are also covered.
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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
- 3. “ A collection of objects connected to each other in some fashion” [Watts, 2002]
- 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 !
- 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
- 28. Next: Interesting discussion points… End of main presentation
- 35. Some interesting bits: Distributed intelligence Ant colony Source: http:// www.youtube.com/watch?v =ozkBd2p2piU URL: http:// www.youtube.com/watch?v =ozkBd2p2piU
- 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: "I wonder if I still have time to go shoot a short film with Kevin Bacon?" URL: http://xkcd.com/599/
Editor's Notes
- 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)
- 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”
- 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.