ILPnet2 social network analysis Miha Grčar Course in Knowledge Management Lecturer: prof. dr. Nada Lavrac Ljubljana, January 2007

Outline of the presentation Data preprocessing Directing the network Social vs. structural prestige Correlation between the two Triad census of strong components in the co-authorship network Hierarchy of authors with respect to co-authorship Conclusions Ljubljana, January 2007 Miha Grčar

Data preprocessing # citations # (joint) publications Ljubljana, January 2007 Miha Grčar

Data preprocessing Pajek network file SQL Ljubljana, January 2007 Miha Grčar

Ljubljana, January 2007 Miha Grčar

Directing the network Create a complete directed network Logarithmize and normalize values Allow each author to keep at most k outgoing arcs – the ones with the highest weights Calculate proximity prestige for several different values of k and a, and determine its correlation with/to the social prestige represented by the number of citations Ljubljana, January 2007 Miha Grčar

Correlation Ljubljana, January 2007 Miha Grčar

Strong components triad census for k=3, a=1 ------------------------------------------------------------------------------------------------------ Type Number of triads (ni) Expected (ei) (ni-ei)/ei Model 3 - 102 0 61.84 -1.00 Balance 16 - 300 0 0.00 -1.00 1 - 003 2985835 2984491.39 0.00 Clusterability 4 - 021D 10 61.84 -0.84 Ranked Clusters 5 - 021U 1534 61.84 23.80 9 - 030T 28 0.33 85.14 12 - 120D 0 0.00 -1.00 13 - 120U 0 0.00 -1.00 2 - 012 44402 47062.30 -0.06 Transitivity 14 - 120C 0 0.00 -1.00 Hierarchical Clusters 15 - 210 0 0.00 -1.00 6 - 021C 55 123.69 -0.56 Forbidden 7 - 111D 0 0.33 -1.00 8 - 111U 0 0.33 -1.00 10 - 030C 0 0.11 -1.00 11 - 201 0 0.00 -1.00 Chi-Square: 37695.2629*** 10 cells (62.50%) have expected frequencies less than 5. The minimum expected cell frequency is 0.00. Ljubljana, January 2007 Miha Grčar

Strong components in k=3, a=1 Net>Hierarchical Decomposition>Symmetric-acyclic (Net>Transform>Remove>Loops) Net>Partitions>Depth>Acyclic --------------------------------------------------------------- Net>Components>Strong - 1st partition: depth partition of the shrunk network - 2nd partition: strong components Partitions>Expand>First according to Second (Shrink) Operations>Transform>Remove Lines>Between Clusters Net>Transform>Arcs->Edges>Bidirected only Ljubljana, January 2007 Miha Grčar

Strong components, hierarchical view Ljubljana, January 2007 Miha Grčar

People, ranked clusters 1. Remove inter-cluster arcs 2. Convert bidirected intra-cluster arcs into edges 3. Remove all remaining arcs Ljubljana, January 2007 Miha Grčar

People, hierarchical view Ljubljana, January 2007 Miha Grčar

Conclusions (Typical) data-mining data preprocessing process was presented We have shown that some directed network models reflect the ranking of authors according to the citations quite well We showed Pajek can be used to explore rankings and hierarchies in social networks Slovene ILP team rocks!  Ljubljana, January 2007 Miha Grčar