Networks and connections

An introduction to theories of complex networks

John Brissenden

15.12.09

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Reading

Barabasi, A-L, and Bonabeau, E (2003), Scale-Free Networks. Scientific American, May 2003

Benkler (2006), chapter 7

Terranova (2004), chapter 2

http://www.barabasilab.com/index.php

Learning outcomes

To understand the non-random characteristics of complex networks

To apply theoretical models to the www and to social networks

To consider implications for public relations

Random and scale-free networks

Normal and power-law distribution

Benkler (2006): 244

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Barabasi and Albert (1999)The probability that any node on the network will be very highly connected to many others is VERY LOW

The probability that a very large number of nodes will be connected very loosely or not at all is VERY HIGH

Preferential attachment: new nodes prefer to attach to well-attached nodes

Huberman and Adamic (1999)

Each website has an intrinsically different growth rate

New sites are formed at an exponential rate

PREFERENTIAL ATTACHMENT + GROWTH = ?

black: opinion leadersred: influenced green: uninfluenced grey: undecided

Viral marketing

http://www.orgnet.com

Hubs:

‘broadcast’ weakly infectious viruses,

ideas

ImplicationsThe more popular you are, the more popular you become

Niches are important

Older nodes (sites) tend to be more popular than new ones, but only on average

Money alone is not enough to guarantee future popularity or growth, but relevance and connection to already popular nodes can be

Clustering

Sites cluster into densely-linked regions or communities of interest

They link much more to each other than to nodes outside

Clustering increases and intensifies as you move along the “long tail”

28%: heavily 28%: heavily interlinked: interlinked:

multiple multiple redundant redundant

pathspaths

28%: heavily 28%: heavily interlinked: interlinked:

multiple multiple redundant redundant

pathspaths

22%: link to 22%: link to core, but not core, but not

from core; new, from core; new, or lower-or lower-

interest sitesinterest sites

22%: link to 22%: link to core, but not core, but not

from core; new, from core; new, or lower-or lower-

interest sitesinterest sites 22%: link from 22%: link from core, but not to core, but not to

core; doc core; doc depositories or depositories or

internal org internal org sitessites

22%: link from 22%: link from core, but not to core, but not to

core; doc core; doc depositories or depositories or

internal org internal org sitessites

22%: cannot 22%: cannot reach or be reach or be

reached from reached from corecore

22%: cannot 22%: cannot reach or be reach or be

reached from reached from corecore

10%: entirely 10%: entirely isolatedisolated

10%: entirely 10%: entirely isolatedisolated

Benkler (2006): 248-9

Benkler (2006): 252

Distribution becomes more normal in smaller clusters

Summary

“Bow tie” model repeats itself within clusters

As clusters become smaller, attention is more evenly spread

Very very few are receiving no attention at all

The small worlds effect