Todays topics Networks Definitions Modeling Analysis Slides from

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. Comp. Sci 001 11. 1

Emerging science of networks l l Examining apparent similarities between many human and technological systems & organizations ä Importance of network effects in such systems How things are connected matters greatly ä Structure, asymmetry and heterogeneity 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 A revolution of ä measurement ä theory ä breadth of vision Comp. Sci 001 (M. Kearns) 11. 2

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? 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? ) Comp. Sci 001 11. 3

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, …, vn-1 is a path where vk and vk+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 Comp. Sci 001 78 NYC Phil 268 204 190 Wash DC LGA $412 Boston 394 $441 $186 LAX $1701 DCA $186 ORD 11. 4

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 Visit all vertices without repeating? Visit all edges? ä With minimal cost? Hard! What are the properties of the network? ä Structural: Is it connected? ä Statistical: What is the average number of neighbors? l l Comp. Sci 001 11. 5

Six Degrees of Bacon l Background Ø Stanley Milgram’s Six Degrees of Separation? Ø Craig Fass, Mike Ginelli, and Brian Turtle invented it as a drinking game at Albright College Ø Brett Tjaden, Glenn Wasson, Patrick Reynolds have run t online website from UVa and beyond Ø 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? Ø How does it answer these requests? Comp. Sci 001 11. 6

How does the Oracle work? l l Not using Oracle™ Queries require traversal of the graph BN = 1 Sean Penn BN = 0 Kevin Bacon Mystic River Apollo 13 Footloose Comp. Sci 001 Tim Robbins Tom Hanks Bill Paxton Sarah Jessica Parker John Lithgow 11. 7

How does the Oracle Work? l l BN = Bacon Number Queries require traversal of the graph BN = 2 Woody Allen BN = 1 Sean Penn Mystic River BN = 0 Tim Robbins Tom Hanks Kevin Bacon Apollo 13 Footloose Bill Paxton Sarah Jessica Parker John Lithgow Comp. Sci 001 Sweet and Lowdown Judge Reinhold Fast Times at Ridgemont High War of the Worlds Miranda Otto The Shawshank Redemption Morgan Freeman Cast Away Helen Hunt Forrest Gump Tombstone A Simple Plan Sally Field Val Kilmer Billy Bob Thornton 11. 8

How does the Oracle work? l l How do we choose which movie or actor to explore next? Queries require traversal of the graph BN = 2 Woody Allen BN = 1 Sean Penn Mystic River BN = 0 Tim Robbins Tom Hanks Kevin Bacon Apollo 13 Footloose Bill Paxton Sarah Jessica Parker John Lithgow Comp. Sci 001 Sweet and Lowdown Judge Reinhold Fast Times at Ridgemont High War of the Worlds Miranda Otto The Shawshank Redemption Morgan Freeman Cast Away Helen Hunt Forrest Gump Tombstone A Simple Plan Sally Field Val Kilmer Billy Bob Thornton 11. 9

Center of the Hollywood Universe? l l l 1, 018, 678 people can be connected to Bacon Is he the center of the Hollywood Universe? ä Who is? ä Who are other good centers? ä What makes them good centers? 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 ä Degree: the degree of a node Betweenness: a measure of how much a vertex is between other nodes Comp. Sci 001 11. 10

Oracle of Bacon l l l Name someone who is 4 degrees or more away from Kevin Bacon 1 4 2 5 3 6 What characteristics makes someone farther away? What makes someone a good center? Is Kevin Bacon a good center? Comp. Sci 001 11. 11

Business & Economic Networks l l Example: e. Bay bidding ä vertices: e. Bay users ä links: represent bidder-seller or buyer-seller ä fraud detection: bidding rings Example: corporate boards ä vertices: corporations ä links: between companies that share a board member Example: corporate partnerships ä vertices: corporations ä links: represent formal joint ventures Example: goods exchange networks ä vertices: buyers and sellers of commodities ä links: represent “permissible” transactions Comp. Sci 001 (M. Kearns) 11. 12

Enron Comp. Sci 001 11. 13

Physical Networks l l l Example: the Internet ä vertices: Internet routers ä links: physical connections ä vertices: Autonomous Systems (e. g. ISPs) ä links: represent peering agreements ä latter example is both physical and business network Compare to more traditional data networks Example: the U. S. power grid ä vertices: control stations on the power grid ä links: high-voltage transmission lines ä August 2003 blackout: classic example of interdependence Comp. Sci 001 (M. Kearns) 11. 14

US Power Grid Comp. Sci 001 11. 15

Content Networks l l Example: Document similarity ä Vertices: documents on web ä Edges: Weights defined by similarity ä See Touch. Graph Google. Browser Conceptual network: thesaurus ä Vertices: words ä Edges: synonym relationships Comp. Sci 001 11. 16

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 How do we navigate in such networks? l Comp. Sci 001 11. 17

Acquaintanceship & more Comp. Sci 001 11. 18

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 Comp. Sci 001 11. 19

�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? Comp. Sci 001 11. 20

Types of networks l l Pick a class of network: 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? Comp. Sci 001 11. 21

Graph properties l Max Degree? l Center? Comp. Sci 001 11. 22