Scale Free and Small Worlds Networks: Studying A-Synchronous Discussion Groups Gilad Ravid Open University of Israel & Haifa University

Asynchronous discussion groups as Small World and Scale Free Networks by Gilad Ravid and Sheizaf Rafaeli September Issue first pick September Issue first pick e9_9/ravid/index.html e9_9/ravid/index.html

Social Network Analysis

SNA  Network analysis is the study of social relations among a set of actors. It is a field of study -- a set of phenomena or data which we seek to understand

Small World Networks  Two characteristics A small average path length A small average path length Mean shortest node-to-node pathMean shortest node-to-node path A large clustering coefficient A large clustering coefficient How many of a node’s neighbors are connected to each otherHow many of a node’s neighbors are connected to each other

Scale Free Networks  Scale-free networks are characterized by a power-law distribution of a node’s degree.

Some Published Networks ( adapted from Newman 2003 ) CαlZmn ,516, ,913U film actors film actors ,3927,673U company directors company directors ,489253,339U math coauthorship math coauthorship / ,30059,912D messages 3.22,810U sexual contacts sexual contacts / ,6358,830D Discussion Groups ,000, ,902U Word co- occurrence Word co- occurrence info ,99210,697U Internet tech ,5944,941U power grid power grid ,359307D Neural networks Neural networks bio social

Kevin Bacon Shoshi Marciano Sassi Keshet Jason Patric Kevin Bacon Nisuim Nusah Tel Aviv, 1979 The Beast of War,1988 Sleepers, 1996

Neural network of C. Elegans

Syphilis Transmission in Georgia

Corporate Partnerships

Internet Connections (CAIDA)

Linking language lexicon

Power Transmission Grid of Western US

Small World Networks Affects  CPL -> Information percolation / Speed of Diffusion  Cliquishness  Personal problems Find jobs Find jobs Find information / answers Find information / answers  Group problems Disasters recovery Disasters recovery Inventions Inventions  Group decision making  Hard to forecast network dynamics

Scale-Free Networks  …. are common  … important category in networks study  Have very connected members (Hubs)  Hubs have a key role  ….results of self organized network  … growth with preferential attachment mechanism

Scale Free Networks Affects  Continuous hierarchy of members  No characterized member  Resistance to failure  Sensitivity to attacks  We know how they form  Information diffusion  Rich get richer

Research Sample  Discussion groups of more than 400 courses  Courses taught  158,276 messages

Why discussion groups?  The main carriage for cooperative learning and working  Knowledge management  Sage on the Stage to Guide on the Side  Shared memory (space)  Equal opportunity to read and write messages  Message are the links between participants and knowledge  One can read (lurk) other discussions

Research populations Percentage of Number The Population A100%75,409 All Registered Participants A A16.5%12,506 Participants who sent at least 1 message B B28.8%3,609 Non active Participants (received no answers and did not answer others) C B0.5%67 Participants who only answered themselves D B70.6%8,830 Regular Participants E

Sig. RR2R2 b1b1 b0b0 Model Output Degree Input Degree All Degree

CCCPL Discussion Groups Network Random Network (Average encompassing three networks) Theoretical Random Network Ratio between random network and discussion groups

Creation of a scale-free net  Growth and preferential attachment

Scale-Free Networks: Mechanisms 1. Growth 2. Preferential Attachment

Gilad Ravid