1. CompSci 001 11.1 Today’s topics Networks ä Definitions ä Modeling ä Analysis ä Slides from Michael Kearns - Univ. of Pennsylvania ä Slides from Patrick Reynolds – Duke CS 2007 Reading Kearns, Michael. "Economics, Computer Science, and Policy." Issues in Science and Technology, Winter 2005.

2. CompSci 001 11.2 Emerging science of networks l Examining apparent similarities between many human and technological systems & organizations ä Importance of network effects in such systems l How things are connected matters greatly ä Structure, asymmetry and heterogeneity l Details of interaction matter greatly ä The metaphor of viral spread ä Dynamics of economic and strategic interaction ä Qualitative and quantitative; can be very subtle l A revolution of ä measurement ä theory ä breadth of vision (M. Kearns)

3. CompSci 001 11.3 Graphs: Structures and Algorithms l How do packets of bits/information get routed on the internet ä Message divided into packets on client (your) machine ä 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? ä Routing tables store local information, not global (why?) l What about The Oracle of Bacon, Erdos Numbers, and Word Ladders?The Oracle of BaconErdos Numbers ä All can be modeled using graphs ä What kind of connectivity does each concept model? l Graphs are everywhere in the world of algorithms (world?)

4. CompSci 001 11.4 Vocabulary l Graphs are collections of vertices and edges (vertex also called node) ä Edge connects two vertices Direction can be important, directed edge, directed graph Edge may have associated weight/cost l A vertex sequence v 0, v 1, …, v n-1 is a path where v k and v k+1 are connected by an edge. ä If some vertex is repeated, the path is a cycle ä A graph is connected if there is a path between any pair of vertices NYC Phil Boston Wash DC 204 78 190 268 394 LGALAX ORD DCA $186 $412 $1701 $441

5. CompSci 001 11.5 Network/Graph questions/algorithms l What vertices are reachable from a given vertex? ä Two standard traversals: depth-first, breadth-first ä Find connected components, groups of connected vertices l Shortest path between any two vertices (weighted graphs?)! l Longest path in a graph ä No known efficient algorithm ä Longest shortest path: Diameter of graph l Visit all vertices without repeating? Visit all edges? ä With minimal cost? Hard! l What are the properties of the network? ä Structural: Is it connected? ä Statistical: What is the average number of neighbors?

6. CompSci 001 11.6 Six Degrees of Bacon l 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 l http://oracleofbacon.org handles 2 kinds of requests 1. Find the links from Actor A to Actor B. 2. How good a center is a given actor?  How does it answer these requests?

7. CompSci 001 11.7 How does the Oracle work? l Not using Oracle™ l 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

8. 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 = 1 Sweet 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 l BN = Bacon Number l Queries require traversal of the graph

9. 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 = 1 Sweet 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 13 Kevin Bacon l How do we choose which movie or actor to explore next? l Queries require traversal of the graph

10. CompSci 001 11.10 Center of the Hollywood Universe? l 1,018,678 people can be connected to Bacon l Is he the center of the Hollywood Universe? ä Who is? ä Who are other good centers? ä What makes them good centers? l Centrality ä 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. ä Degree: the degree of a node ä Betweenness: a measure of how much a vertex is between other nodes

11. CompSci 001 11.11 Oracle of Bacon l Name someone who is 4 degrees or more away from Kevin Bacon 14 25 36 l What characteristics makes someone farther away? l What makes someone a good center? Is Kevin Bacon a good center?

12. CompSci 001 11.12 Business & Economic Networks l Example: eBay bidding ä vertices: eBay users ä links: represent bidder-seller or buyer-seller ä fraud detection: bidding rings l Example: corporate boards ä vertices: corporations ä links: between companies that share a board member l Example: corporate partnerships ä vertices: corporations ä links: represent formal joint ventures l Example: goods exchange networks ä vertices: buyers and sellers of commodities ä links: represent “permissible” transactions (M. Kearns)

13. CompSci 001 11.13 Enron

14. CompSci 001 11.14 Physical Networks l Example: the Internet ä vertices: Internet routersInternet routers ä links: physical connections ä vertices: Autonomous Systems (e.g. ISPs)Autonomous Systems ä links: represent peering agreements ä latter example is both physical and business network l Compare to more traditional data networkstraditional data networks l Example: the U.S. power gridU.S. power grid ä vertices: control stations on the power grid ä links: high-voltage transmission lines ä August 2003 blackout: classic example of interdependenceinterdependence (M. Kearns)

15. CompSci 001 11.15 US Power Grid

16. CompSci 001 11.16 Content Networks l Example: Document similarity ä Vertices: documents on web ä Edges: Weights defined by similarity ä See TouchGraph GoogleBrowser l Conceptual network: thesaurus ä Vertices: words ä Edges: synonym relationships

17. CompSci 001 11.17 Social networks l Example: Acquaintanceship networks ä vertices: people in the world ä links: have met in person and know last names ä hard to measure l Example: scientific collaboration ä vertices: math and computer science researchers ä links: between coauthors on a published paper ä Erdos numbers : distance to Paul Erdos ä Erdos was definitely a hub or connector; had 507 coauthors l How do we navigate in such networks?

18. CompSci 001 11.18 Acquaintanceship & more

19. CompSci 001 11.19 Network Models (Barabasi) l Differences between Internet, Kazaa, Chord ä Building, modeling, predicting l Static networks, Dynamic networks ä Modeling and simulation l Random and Scale-free ä Implications? l Structure and Evolution ä Modeling via Touchgraph

20. CompSci 001 11.20 What’s a web-based social network? l Accessible over the web via a browser l Users explicitly state relationships ä Not mined or inferred l Relationships visible and browsable by others ä Reasons? l Support for users to make connections ä Simple HTML pages don’t suffice l Why are they so darn popular? What’s Web 2.0?

21. CompSci 001 11.21 Types of networks l Pick a class of network: l Give a real-world example of such a network: ä What are the vertices (nodes)? ä What are the edges (links)? ä How is the network formed? Is it decentralized or centralized? Is the communication or interaction local or global? ä What is the network's topology? For example, is it connected? What is its size? What is the degree distribution?

22. CompSci 001 11.22 Graph properties l Max Degree? l Center?