The Structure of Scientific Collaboration Networks by M. E. J. Newman CMSC 601 Paper Summary Marie desJardins January 27, 2009

Outline Overview Social networks Scientific collaboration networks  Properties  Data sets Results Conclusions

Overview Computationally analyze scientific collaboration networks Uses actual data sets from online archives Findings:  small-world property  presence of “clustering”  power law distribution of #collaborators, #papers  different patterns in different fields

Social Networks Idea: Represent acquaintanceship relationships between individuals  Measure graph-theoretic properties Widely studied in social science Penny Peter Sergei Lise David Marie

Degree (# edges)  z(Marie) = 4  z = 3 Degree distribution = [2, 2, 3, 3, 4, 4] Clustering  C = probability (ij | ik, jk) = 12/20 =.6 Degree of separation (path length)  average = 1.47  random graph  log N / log z (typically 6) Properties of Social Networks Penny Peter Sergei Lise David Marie

Scientific Collaboration Networks Represent co-authorship relationships Data sets:  Biomedical research (MEDLINE)  Theoretical physics (Los Alamos e-Print Archive (arxiv))  High-energy physics (SPIRES)  Computer science (NCSTRL) Papers from  13K – 2M papers

Erdös Number Paul Erdös  Famous Hungarian mathematician  Published over 1400 papers!  Erdös Number = co-authorship distance to Erdös  Marie’s Erdös Number = ??

Counting Authors Ambiguity in names (first name vs. first initial vs. all initials)  Two counts: all initials vs. 1 st initial   Upper/lower bounds on number of authors

General Properties Average number of papers per author: 4 Average number of authors per paper: 3  Max: 1681!! (SPIRES) Average number of collaborators:  Ranges from 4 (high-energy theory) to 173 (SPIRES) Size of largest connected component:  Ranges from 60% (CS) to 90% (astrophysics) Amount of clustering:  Ranges from 7% (MEDLINE) to 73% (SPIRES)

Degree Distribution Earlier work showed power law distribution of degree (would be straight line) Here we see a power law distribution with an exponential cutoff  Conjecture: result of limited time window, and limited publication life of scientists

Degrees of Separation Average degree of separation  6  “Small world” property – comparable to distance in random graph Diameter (max distance) typically around 20  (for largest connected component)

Summary Scientific collaboration networks  Social networks exhibiting interesting structure  Lots of available data Key characteristics  High clustering  Small-world property  Power-law distribution of #authors, #papers  Properties vary across fields