This document discusses theories of complex networks. It introduces scale-free networks and preferential attachment, where new nodes are more likely to connect to already well-connected nodes, resulting in a power-law distribution. This means most nodes have few connections while a few "hub" nodes have many connections. Viral marketing can spread through these hubs. Networks tend to cluster into communities with dense internal linking. The "bow tie" model shows how attention is distributed across a network in clusters within clusters.

1. Networks and
connections
An introduction to theories of complex networks
John Brissenden
15.12.09

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4. 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

5. 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

15. Random and scale-free networks

16. Normal and power-law distribution
Benkler (2006): 244

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19. 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

20. Huberman and Adamic (1999)
Each website has an intrinsically different growth rate
New sites are formed at an exponential rate
PREFERENTIAL ATTACHMENT + GROWTH = ?

22. Viral marketing
Hubs:
‘broadcast’ weakly
infectious viruses,
ideas
black: opinion leaders
red: influenced
green: uninfluenced
grey: undecided
http://www.orgnet.com

23. Viral marketing
Hubs:
‘broadcast’ weakly
infectious viruses,
ideas
black: opinion leaders
red: influenced
green: uninfluenced
grey: undecided
http://www.orgnet.com

24. Implications
The 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

25. 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”

26. 28%:
22%: link to core, but heavily interlinked:
not from core; new, or multiple redundant
lower-interest sites paths
22%: link from
core, but not to core;
doc depositories or
internal org sites
22%: cannot reach or be
reached from core
10%: entirely isolated
Benkler (2006): 248-9

27. Distribution becomes more normal in smaller clusters
Benkler (2006): 252

28. 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

29. The small worlds effect