What Is A Network?(and why do we care?)

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 2

“A collection of objects (nodes)

connected to each other in some

fashion” - Watts, 2002

Network Defined

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 3

• An agent/object's actions are

affected by the actions of

others around it.

•Actions/choices are not made in

isolation, i.e., they are contingent on the actions and choices of others

In A Network …

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 4

The Internet

Neural Networks (computer & human)

Proteins and Genes

Stem cells (and other cells)

Diseases

Social Groups

Examples of Networks

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 5

• Theory-> from “fixed” to “dynamic”

• “real networks represent populations of

individual components that are actually

doing something” - Watts, 2002

• Networks are key to understanding non-

linear, dynamic systems

Networks

Britain From Above (http://www.bbc.co.uk/britainfromabove)

Data Networks

Terms

• Node = individual components of a network, e.g. people, power stations, links• Edge = direct link between components (referred to as a dyad in context of social networks, a relationship between two people)• Path = route taken to connect two nodes. “Six degrees of separation” average path length = 6

http://blog.linkedin.com/2011/01/24/linkedin-inmaps/

Human Networks

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 9

• Began in 1967 at Harvard University• Sent packages to randomly selected people in

Omaha, Nebraska & Wichita and asked that they

be delivered to individuals in Boston,

Massachusetts• Could only forward to people they knew on a first-

name basis• 64 of 296 letters reached their destination• Average path length of these was around 5.5 or 6

Milgram’s Experiment

Unclustered Network

Clustered Network

Types of Networks

1. Grid/lattice network(structure, order)

2. Small-world network(a mix of order and randomness)

3. Random network(randomness)

Power Law

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 14

• Power law distributions tend to arise in social systems where many people express their preferences among many options. • As the number of options rise, the curve becomes more extreme.• Most elements in a power law system are below average (the “long tail”)

Shirky On Power Law

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 15

“Alice, the first user, chooses her blogs unaffected by anyone else, but Bob has a slightly higher chance of liking Alice's blogs than the others. When Bob is done, any blog that both he and Alice like has a higher chance of being picked by Carmen, and so on, with a small number of blogs becoming increasingly likely to be chosen in the future because they were chosen in the past.”

Shirky On Power Law

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 16

“Within a social network, weak ties

…are indispensable to

individuals’ opportunities

and to their incorporation

into communities while strong

ties breed local cohesion.”(Mark Granovetter, 1973)

Networks : Weak Ties

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 17

• The stronger the tie between two people, the more similar they are, in various ways (Mark Granovetter, 1973)

• Weak ties = “friends of friends” • Weak ties provide a bridge between social circles, access to information and resources beyond my “tight” social circle

Networks : Weak Ties

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 18

“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]

Weak Ties Are Powerful

An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 19

Over time, we are more likely to

become acquainted if we have

something in common• this bias towards the familiar reduces the

pure randomness of connections• “homophily” or “birds of a feather flock

together”

Strong Tie Truism

California: F500 Companies

http://flickr.com/photos/11242012@N07/1363558436

TheyRule.Net

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• Large scale• Continual growth• Distributed, organic growth: vertices “decide” who to link to• A mixture of local and long-distance connections• Interaction (largely) restricted to links• Abstract notions of distance: geographical, content, social…

Informal Properties : The Web

• Reaction to “your friends have more friends

than you do” (friends paradox - TED talk)

• What does a highly “spreadable”

(viral) idea look like? (RickRolling as a meme)

• How might we actively seek new ideas/voices?

What is the role of software here?

Discussion

Credits

• Kathy E Gill, @kegill, CC share-share-alike, non-commercial• Sources:

– Duncan Watts, Six Degrees of Separation– Kyle Findlay, SAMRA 2010 Conference presentation– Michael Kearns, Social Network Theory