CompSci 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.

CompSci 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)

CompSci 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?)

CompSci 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 LGALAX ORD DCA $186 $412 $1701 $441

CompSci 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?

CompSci 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 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?

CompSci 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

CompSci 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

CompSci 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

CompSci 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

CompSci Oracle of Bacon l Name someone who is 4 degrees or more away from Kevin Bacon l What characteristics makes someone farther away? l What makes someone a good center? Is Kevin Bacon a good center?

CompSci 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)

CompSci Enron

CompSci 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)

CompSci US Power Grid

CompSci 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

CompSci 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?

CompSci Acquaintanceship & more

CompSci 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

CompSci 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?

CompSci 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?

CompSci Graph properties l Max Degree? l Center?