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?