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CompSci 001 11.1
Today’s topics
Networks Definitions Modeling Analysis Slides from Michael Kearns - Univ. of
Pennsylvania Slides from Patrick Reynolds – Duke CS 2007
ReadingKearns, Michael. "Economics, Computer Science,
and Policy." Issues in Science and Technology, Winter 2005.
CompSci 001 11.2
Emerging science of networks Examining apparent similarities between many human
and technological systems & organizations Importance of network effects in such systems
How things are connected matters greatly Structure, asymmetry and heterogeneity
Details of interaction matter greatly The metaphor of viral spread Dynamics of economic and strategic interaction Qualitative and quantitative; can be very subtle
A revolution of measurement theory breadth of vision
(M. Kearns)
CompSci 001 11.3
Graphs: Structures and Algorithms How do packets of bits/information get routed on the
internet Message divided into packets on client (your) machine Packets sent out using routing tables toward
destination• Packets may take different routes to destination• What happens if packets lost or arrive out-of-order?
Routing tables store local information, not global (why?)
What about The Oracle of Bacon, Erdos Numbers, and Word Ladders? All can be modeled using graphs What kind of connectivity does each concept model?
Graphs are everywhere in the world of algorithms (world?)
CompSci 001 11.4
Vocabulary Graphs are collections of
vertices and edges (vertex also called node) Edge connects two
vertices• Direction can be
important, directed edge, directed graph
• Edge may have associated weight/cost
A vertex sequence v0, v1, …, vn-1 is a path where vk and vk+1 are connected by an edge. If some vertex is
repeated, the path is a cycle
A graph is connected if there is a path between any pair of vertices
NYC Phil
BostonWash DC
204
78
190
268
394
LGA LAX
ORDDCA $186
$186
$412 $1701
$441
CompSci 001 11.5
Network/Graph questions/algorithms What vertices are reachable from a given vertex?
Two standard traversals: depth-first, breadth-first Find connected components, groups of connected
vertices
Shortest path between any two vertices (weighted graphs?)!
Longest path in a graph No known efficient algorithm Longest shortest path: Diameter of graph
Visit all vertices without repeating? Visit all edges? With minimal cost? Hard!
What are the properties of the network? Structural: Is it connected? Statistical: What is the average number of neighbors?
CompSci 001 11.6
Six Degrees of Bacon
Background Stanley Milgram’s Six Degrees of Separation? Craig Fass, Mike Ginelli, and Brian Turtle invented it
as a drinking game at Albright College Brett Tjaden, Glenn Wasson, Patrick Reynolds have
run t online website from UVa and beyond Instance of Small-World phenomenon
http://oracleofbacon.org handles 2 kinds of requests1. Find the links from Actor A to Actor B. 2. How good a center is a given actor? How does it answer these requests?
CompSci 001 11.7
How does the Oracle work? Not using Oracle™ Queries require traversal of the graph
BN = 0 Mystic River
Apollo 13
Footloose
John Lithgow
Sarah Jessica Parker
Bill Paxton
Tom Hanks
Sean Penn
Tim Robbins
BN = 1
Kevin Bacon
CompSci 001 11.8
How does the Oracle Work?
Kevin Bacon
Mystic River
Apollo 13
Footloose
John Lithgow
Sarah Jessica Parker
Bill Paxton
Tom Hanks
Sean Penn
Tim Robbins
BN = 0
BN = 1Sweet and Lowdown
Fast Times at Ridgemont High
War of the Worlds
The Shawshank Redemption
Cast Away
Forrest Gump
Tombstone
A Simple Plan
Morgan Freeman
Sally Field
Helen Hunt
Val Kilmer
Miranda Otto
Judge Reinhold
Woody Allen
Billy Bob Thornton
BN = 2
BN = Bacon Number Queries require traversal of the graph
CompSci 001 11.9
How does the Oracle work?
Mystic River
Footloose
John Lithgow
Sarah Jessica Parker
Tom Hanks
Sean Penn
Tim Robbins
BN = 0
BN = 1Sweet and Lowdown
Fast Times at Ridgemont High
War of the Worlds
The Shawshank Redemption
Cast Away
Forrest Gump
A Simple Plan
Morgan Freeman
Sally Field
Helen Hunt
Miranda Otto
Judge Reinhold
Woody Allen
Billy Bob Thornton
BN = 2
Bill Paxton
Tombstone
Val Kilmer
Apollo 13Kevin Bacon
How do we choose which movie or actor to explore next?
Queries require traversal of the graph
CompSci 001 11.10
Center of the Hollywood Universe? 1,018,678 people can be connected to Bacon Is he the center of the Hollywood Universe?
Who is? Who are other good centers? What makes them good centers?
Centrality Closeness: the inverse average distance of a
node to all other nodes• Geodesic: shortest path between two vertices • Closeness centrality: number of other vertices
divided by the sum of all distances between the vertex and all others.
Degree: the degree of a node Betweenness: a measure of how much a vertex
is between other nodes
CompSci 001 11.11
Oracle of Bacon
Name someone who is 4 degrees or more away from Kevin Bacon1 42 53 6
What characteristics makes someone farther away?
What makes someone a good center? Is Kevin Bacon a good center?
CompSci 001 11.12
Business & Economic Networks Example: eBay bidding
vertices: eBay users links: represent bidder-seller or buyer-seller fraud detection: bidding rings
Example: corporate boards vertices: corporations links: between companies that share a board
member Example: corporate partnerships
vertices: corporations links: represent formal joint ventures
Example: goods exchange networks vertices: buyers and sellers of commodities links: represent “permissible” transactions
(M. Kearns)
CompSci 001 11.13
Enron
CompSci 001 11.14
Physical Networks Example: the Internet
vertices: Internet routers links: physical connections vertices: Autonomous Systems (e.g. ISPs) links: represent peering agreements latter example is both physical and business network
Compare to more traditional data networks Example: the U.S. power grid
vertices: control stations on the power grid links: high-voltage transmission lines August 2003 blackout: classic example of
interdependence
(M. Kearns)
CompSci 001 11.15
US Power Grid
CompSci 001 11.16
Content Networks
Example: Document similarity Vertices: documents on web Edges: Weights defined by similarity See TouchGraph GoogleBrowser
Conceptual network: thesaurus Vertices: words Edges: synonym relationships
CompSci 001 11.17
Social networks
Example: Acquaintanceship networks vertices: people in the world links: have met in person and know last names hard to measure
Example: scientific collaboration vertices: math and computer science researchers links: between coauthors on a published paper Erdos numbers : distance to Paul Erdos Erdos was definitely a hub or connector; had 507
coauthors How do we navigate in such networks?
CompSci 001 11.18
Acquaintanceship & more
CompSci 001 11.19
Network Models (Barabasi)
Differences between Internet, Kazaa, Chord Building, modeling, predicting
Static networks, Dynamic networks Modeling and simulation
Random and Scale-free Implications?
Structure and Evolution Modeling via Touchgraph
CompSci 001 11.20
What’s a web-based social network?
Accessible over the web via a browser
Users explicitly state relationships Not mined or inferred
Relationships visible and browsable by others Reasons?
Support for users to make connections Simple HTML pages don’t suffice
Why are they so darn popular? What’s Web 2.0?
CompSci 001 11.21
Types of networks Pick a class of network: Give a real-world example of such a network:
What are the vertices (nodes)?
What are the edges (links)?
How is the network formed? Is it decentralized or centralized? Is the communication or interaction local or global?
What is the network's topology? For example, is it connected? What is its size? What is the degree distribution?
CompSci 001 11.22
Graph properties
Max Degree?
Center?