Analyzing Networks

Milgram’s Experiments “Six degrees of Separation” Milgram’s 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

Milgram’s Experiments Properties of Chains or Networks Degrees of Separation between individuals Scores of models have been developed –Six degrees of Kevin Bacon ( –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 – Kruskal’s Algorithm Euler’s 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