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This is a very good presentation by Kyle Findlay. I have added some sources but all the work is by Kyle.

This is a very good presentation by Kyle Findlay. I have added some sources but all the work is by Kyle.

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  • 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.

Network theory Presentation Transcript

  • 1. An Introduction toNetwork TheoryKyle FindlayKyle.Findlay@tns-global.comR&D ExecutiveTNS 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 An Introduction to Network Theory | Kyle Findlay SAMRA 2010
  • 2. An agent/objects actions are affectedby the actions of others around it. What is a network? Actions, choices, etc. are not made in isolation i.e. they are contingent on others actions, choices, etc. An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 3. “A collection of objects connected toeach other in some fashion”[Watts, 2002]
  • 4.  Social groups  Diseases  Stem cells The internet  Neural networks (computer & human)  Other cells Cities  Proteins & genes  Plants Quaking Aspen (one of the largest organisms in the world – these trees represent a single organism with a shared root system) The blogosphere Source: Six Degrees, Duncan Watts, 2002 Proliferation of landlines in LondonWhat is a network? Human genome Rabbit cell An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 5. ▫ 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 the behaviour of the system as a whole Networks used to be thought of as systems… structures ▫ Networks are key to understanding non-linear, dynamic fixed  …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)What is a network? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 6. CAUTION: Gratuitous network shots Data networks Air traffic network Telecommunications networks Shipping (sea) networks Source: Britain From Above (http://www.bbc.co.uk/britainfromabove) An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 7. Network thinking can be appliedalmost anywhere! An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 8. URL: http://www.youtube.com/watch?v=PufTeIBNRJ4 Epidemiology (i.e. spread of diseases) e.g. spread of foot & mouth disease in the UK in 2001 over 75 daysWhere’s it applied? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 9. URL: http://www.youtube.com/watch?v=8C_dnP2fvxk Physics e.g. particle interactions, the structure of the universeWhere’s it applied? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010
  • 10. URL: http://www.youtube.com/watch?v=lRZ2iEHFgGo URL: http://www.youtube.com/watch?v=AEoP-XtJueo 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? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 11. Vid not working URL: http://www.youtube.com/watch?v=l-RoDv7c5ok URL: http://www.youtube.com/watch?v=o4g930pm8Ms Technology e.g. mapping the online world, making networks resilient in the face of cyber-terrorism, optimising cellular networks, controlling air trafficWhere’s it applied? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 12. URL: http://www.youtube.com/watch?v=YadP3w7vkJA URL: http://www.youtube.com/watch?v=Sp8tLPDMUyg Biology e.g. fish swimming in schools, ant colonies, birds flying in formation, crickets chirping in unison, giant honeybees shimmeringWhere’s it applied? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 13. Source: The Human Brain Book by Rita Carter Medicine e.g. cell formation, nervous system, neural networksWhere’s it applied? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 14. URL: http://www.youtube.com/watch?v=9n9irapdON4 URL: http://www.youtube.com/watch?v=sD2yosZ9qDw And, most interestingly…society e.g. interactions between people (e.g. Facebook; group behaviour)Where’s it applied? An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 15. Some terminology… ▫ Node = individual components of a network e.g. people, power stations, neurons, etc. ▫ Edge = direct link between components (referred to as a dyad in context of social networking An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 16. No connections Some nodes All relevant nodes between nodes connected connected c=0 c = 1/3 c=1▫ 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” Important network features: Clustering co-efficient An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 17. “Unclustered” network “Clustered” network None of Ego’s friends know each other* All of Ego’s friends know each other Important network features: Clustering co-efficient*Source: Six Degrees, Duncan Watts, 2002 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 18. ▫ A real-world example: CEOs of Fortune 500 companies  Which companies share directors? Clusters are colour-coded Important network features: Clustering co-efficientSource: http://flickr.com/photos/11242012@N07/1363558436 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 19. ▫ Average path length = the average number of ‘hops’ required to reach any other node in the network ▫ “Six degrees of separation” average path length = 6Important network features:Average path length An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 20. ▫ The degree of a node is the number of connections (or edges) it has coming in from, and going out to, other nodes 1 2 10 3 9 Node 4 8 7 510 connections 6 or “edges” Important network features: Degree distribution An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 21. 3 main types of networks 1. Grid/lattice network 2. Small-world network 3. Random network (structure, order) (a mix of order and randomness) (randomness) β=0 << Level of randomness of links >> β=1They sit on a continuum based on a few factors: 1 Randomness 2 Clustering 3 Ave path length *Source: Six Degrees, Duncan Watts, 2002 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 22. 3 main types of networks:Grid/Lattice network ▫ Simplest form of network with nodes ranged geometrically ▫ Low degree (nodes only connected to closest neighbours) ▫ High clustering ▫ Long average path length (no shortcuts – have to go through all nodes) ▫ Pros: methodical, easy to visualise ▫ Cons: not very good at modeling most real- 1D lattice world networks Molecule Diamond (crystal) lattice Bismuth crystal An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 23. 3 main types of networks:Small world network ▫ Most nodes aren’t neighbours, but they can be reached from every other node by a small number of hops or steps Higher clustering co-efficient than to a few random  i.e. small average path length dueone would expect if connections were made by pure random chance re-wirings − “A small world network, where nodes represent people and edges connect people that know each other, captures the small world phenomenon of strangers being linked by a mutual acquaintance”  Common in nature, including everything from the internet to gene regulatory networks to ecosystems Source: http://en.wikipedia.org/wiki/Small-world_network An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 24. 3 main types of networks:Random network ▫ Lower clustering than small-world networks generally ▫ No “force” or “bias” influencing how links are created between nodes  i.e. probability of creating an edge/link is independent of previous connections An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 25. The big picture Nature ▫ Networks are evident everywhere in nature ▫ In fact, most natural growth Natural growth = evolutionary, iterative growth, where future growth is constrained by previous growth patterns (referred to as path dependence) processes come about due to − i.e. growth follows the network structure network behaviour An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 26. And market research? ▫ Networks better reflect reality and capture complexity i.e. non-linear dynamics ▫ Network theory helps us to better understand:?How will word of my brand permeate through ? How will negative publicity about my brand spread and ? Who are the gatekeepers in a community that my target market? be interpreted? most affect the flow of information? ?How is the market likely to fall out in terms of ? What will the non-linear market share impact be of a specific (Double Jeopardy)? change in the market e.g. change in market share, perceptions, etc. An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 27. And market research?▫ Network theory has been used to understand imagery and market barriers  Adjusting attributes and seeing knock-on effect in network  Using agent-based modeling to model this effect  Useful for word-of-mouth/viral approaches − Watts and Peretti use network theory to increase reach of WOM campaigns  Helps us avoid thinking about things in a vacuum as it takes account of inter-related variables… − … and provides us with counter-intuitive outcomes that we may not have reached on our own An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 28. End of mainpresentationNext: Interestingdiscussion points…
  • 29. ▫ This is a very simple 2D representation of how I roughly visualise information propagating through a network  It is very simple and doesn’t take into account many concepts  But it is a visual aid that helps one to start thinking about interesting bits: Some how A network in action information might spread from person toSource: http://www.funny-games.biz/reaction-effect.html person An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 30. What does a highly “spreadable” idea look like? • 1,636,967 views in two months (as at 25 April 2010) • Performed in front of 75,000 people at Coachella Music Festival (California, April 2010) URL: http://www.youtube.com/watch?v=Q77YBmtd2RwSome interesting bits: How ideas spread
  • 31.  Who spreads ideas? − Watts vs. Gladwell vs. − Mavens/influencers vs. forest fire − Self-organised criticality − K-shell decomposition?Some interesting bits: How ideas spread
  • 32.  Which ideas spread? − Unpredictable − Ideas that “fit”Some interesting bits: How ideas spread
  • 33. ▫ Refers to systems in which many individual agents with limited intelligence and information are able to pool resources to accomplish a goal beyond the capabilities of the individuals… while no single ant knows how toself-interest − e.g. only focused on build an ant colony − e.g. in mind without the bigger picturethe internet has grown organically over time with no single person directing its growth − i.e. no grand designer  This is known as self-organisation and/or emergence, and is a property of complex networks and non-linear, dynamic systemsSome interesting bits:Distributed intelligence An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 34. ▫ Existence of such behaviour in organisms has many implications for social, military and management applications and is one of the most active areas of research today!Some interesting bits:Distributed intelligence diffusion, memes,  Works best in small-world networks  Implications for knowledge An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 35. URL: http://www.youtube.com/watch?v=ozkBd2p2piU Ant colonySome interesting bits:Distributed intelligence Source: http://www.youtube.com/watch?v=ozkBd2p2piU An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 36. ▫ “On average, the first 5 random re-wirings reduce the average path length of the network by one-half, regardless of the size of the network” [Watts, 2002]* Random re-wirings “8” “3” Long average path length Dramatically reduced average path lengthSome interesting bits:Random re-wirings *Source: Six Degrees, Duncan Watts, 2002, p.89 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 37. Some interesting bits:Triadic closure A B C ▫ People are more likely to become acquainted over time when they have something in common  i.e. we have a bias towards the familiar, thus reducing the pure randomness of connections  Known as “homophily” - “birds of a feather flock together” ▫ Network connections don’t arise independently of each other…  …they are influenced by previous connections ▫ If A knows B…  …and B knows C…  …then A is much more likely to know C *Source: Six Degrees, Duncan Watts, 2002, p.58-61 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 38. Some interesting bits:Triadic closure A B C  This is why random re-wirings are so effective at reducing the ave. path length… − …they help connect clusters, or ‘cliques’, that might otherwise exist in isolation  This is the strength of the small-world network: − High clustering and a relatively small amount of random re-wirings allows for a dramatically reduced average path length… − …allowing everyone to connect to everyone else in relatively few steps e.g. “six degrees of separation” *Source: Six Degrees, Duncan Watts, 2002, p.58-61 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 39. Some interesting bits:Triadic closure •This “birds of a feather flock together” effect was modeled by Watts and Strogatz* • They used α (alpha) to represent level of preference to only connect with friends of friends • Low α = strong preference to only connect with friends of friends (triadic closures occur, independent clusters) • High α = connections chosen at random • Small-world networks exist somewhere around the peak (which represents a phase transition) i.e. where clustering is high but average path length is low • To the left of the peak, clusters are just starting to join together • At the peak, everyone is connected • To the right of the peak, connections are lost as wirings become more random *Source: Six Degrees, Duncan Watts, 2002, p.78-79 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 40. ▫ Studies conducted by Stanley Milgram beginning in 1967 at Harvard University ▫ Sent packages to randomly selected people in Omaha, Nebraska & Wichita ▫ Asked that they bedelivered to individuals in Milgram repeated other similar experiments which also received low Boston, Massachusettscompletion rates ▫ Could only forward package to people they knew  However, experiments on the internet have since confirmed the number at 6: on a first-name basis − Facebook application: ▫ Only 64 of 296 letters reached path–=4.5destination Six Degrees average their million users; 5.73 ▫ Average path length of these was around 5.5 or 6 ▫ Milgram never used the phrase “six degrees ofSome interesting bits: separation” himselfSix degrees of separation Source: Wikipedia, Small world experiment Wikipedia, Six degrees of separation An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 41. ▫ The Kevin Bacon game  Aim is to connect all other actors back to Kevin Bacon  Choice of Kevin Bacon is arbitrary – can be applied to most actorsSome interesting bits:Six degrees of separation *Source: Six Degrees, Duncan Watts, 2002 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 42. 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/Some interesting bits:Six degrees of separation
  • 43. ▫ A network is considered “scale-free” if its degree distribution follows a power law  i.e. nodes can have an unlimited number of links to them e.g. the internet This is what a power law distribution looks like*  A few nodes have many links, while the majority have few links If you take the log of both axes, you should get a straight line*Some interesting bits:Scale-free networks & power laws *Image source: Six Degrees, Duncan Watts, 2002 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 44. ▫ However, very few, if any, networks can display scale-free properties indefinitely  At some point, limited resources force a cut-off e.g. limited number of computers in the world ▫ Therefore, generally, scale-free networks only Taking the log-log of a display a power law distributionlaw distribution line* area of power for some should show a straight the graph However, in practice, the line is generally only straight for some area of the graph*Some interesting bits:Scale-free networks & power laws *Image source: Six Degrees, Duncan Watts, 2002 An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 45. ▫ Power law distributions help us understand natural growth (e.g. popularity of brands, trends, ideas, politics, religion, etc.)  Growth in an environment where social influence occurs tends to result in a power law distribution (think cumulative advantage)  This comes about due to network behaviour  e.g. nodes with more connections are more likely to have even more connections (sounds a lot like… Double Jeopardy!) ▫ This ‘skewing’ of growth patterns is characteristicSome interesting bits:Scale-free networks & power laws of small world networks and results in a few large components and many small components An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 |
  • 46. •Software examples… http://www.youtube.com/watch?v=tYQovmtO06k&feature=related
  • 47. •Thanks!It’s a small world after all  http://www.youtube.com/watch?v=tYQovmtO06k&feature=related