Analyzing Networks Milgrams Experiments Six degrees of Separation Milgrams letters to various recruits in Nebraska who were asked to forward the letter to a stockbroker living at a specified location in MA Participants could only pass the letters (by hand) to personal acquaintances who they thought might be able to reach the target Directly or via a "friend of a friend Three letters reached the destination Milgrams Experiments Properties of Chains or Networks Degrees of Separation between individuals Scores of models have been developed Six degrees of Kevin Bacon (http://oracleofbacon.org/) Erdos Number Networks in Real World (1) Computer Networks Food Chain Structure of Websites Networks in Real World (2) Dating in High School Why Study Networks ? Studying complex relationships (not possible to do this by reducing them to component clusters) Inferring behavior from network properties Understanding functions of networks Graphs (Basics) Two simple concepts Node or Vertex Edge Directed Graphs Node Properties Node Degrees Number of edges connected to a node Average number of edges/node For Directed Graphs in-degree and out- degrees can be calculated Betweenness Centrality Minimum Spanning Tree Kruskals Algorithm Eulers Circuit Network Properties Long tail behavior Few nodes in the network are very well connected (stars of the network) Also known as Power Law Behavior Large number of nodes have very few connections Major implications in marketing, disease control, airport design etc Most Airlines have a few hubs which are very well connected to other hubs Examples of Long Tail Structure of the Internet Examples of Long Tail (2) Structure of an Organization Santa Fe Institute Examples of Long Tail (3) Marketing/Spread of Ideas black: opinion leaders red: influenced green: uninfluenced grey: undecided Day 1Day 2Day 3Day 4Day 5Day 6Day 7Day 8Day 1Day 2Day 3Day 4Day 5Day 6Day 7Day randomly chosen users500 most active users How To Build Networks By Hand Simple networks are possible, large networks become cumbersome Tools JUNG ( Prefuse