Today’s topics
Previous
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Graphs
• Definitions
• Connectedness
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
Oracle of Bacon
Types of Networks
Example Networks
Small Worlds
Centrality: Closeness, Degree, & Betweenness
centrality
Acknowledgements
Lada Adamic, James Moody
The Science of Networks
2.1
Email Communication Network
The Science of Networks
2.2
Political Blog Links at 2004 Election
The Science of Networks
2.3
Viral Spread
The Science of Networks
2.4
The Internet, December 1970
The Science of Networks
2.5
Baseball: Payroll vs. Performance
The Science of Networks
2.6
Milgram Experiment
The Science of Networks
2.7
IM Communication
The Science of Networks
2.8
Degree Centrality
Actor with the most ties is the most important
CD = d(v i ) = å eij
j

where eij is 1 if an vi and vj are
adjacent, 0 otherwise
A purely local measure
The Science of Networks
2.9
Closeness Centrality
An actor is important if she is relatively close to all
other actors
-1
é
ù
Cc (v i ) = êå d(v i ,v j )ú
êë j
úû

where d(x,y) is the length of shortest
path between x and y
Jordan Centrality uses the inverse of the length of the
longest path to any other vertex
The Science of Networks
2.10
Betweenness Centrality
An actor who lies on communication paths can control
communication flow, and is thus important
CB (v i ) = å g jk (v i ) /g jk
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where gjk = the number of geodesics
connecting jk, and gjk(vi) = the number
j<k
that actor i is on.
Information Centrality uses all paths in the network, and
weights them based on their length.
The Science of Networks
2.11
HW1
1.
Network Construction Project Part 1
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
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1.
Identify source of real-world data
Define the nodes and edges
Describe how you will extract data to create network
Textbook Problems

Ch. 2, 1-3
The Science of Networks
2.12