Matrix: SNAP/ca-AstroPh
Description: Collaboration network of Arxiv Astro Physics
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| (undirected graph drawing) |
 |
 |
| Matrix properties | |
| number of rows | 18,772 |
| number of columns | 18,772 |
| nonzeros | 396,160 |
| # strongly connected comp. | 290 |
| explicit zero entries | 0 |
| nonzero pattern symmetry | symmetric |
| numeric value symmetry | symmetric |
| type | binary |
| structure | symmetric |
| Cholesky candidate? | no |
| positive definite? | no |
| author | J. Leskovec, J. Kleinberg and C. Faloutsos |
| editor | J. Leskovec |
| date | 2003 |
| kind | undirected graph |
| 2D/3D problem? | no |
| Additional fields | size and type |
| nodename | full 18772-by-1 |
Notes:
Networks from SNAP (Stanford Network Analysis Platform) Network Data Sets,
Jure Leskovec http://snap.stanford.edu/data/index.html
email jure at cs.stanford.edu
Astro Physics collaboration network
Dataset information
Arxiv ASTRO-PH (Astro Physics) collaboration network is from the e-print arXiv
and covers scientific collaborations between authors papers submitted to Astro
Physics category. If an author i co-authored a paper with author j, the graph
contains a undirected edge from i to j. If the paper is co-authored by k
authors this generates a completely connected (sub)graph on k nodes.
The data covers papers in the period from January 1993 to April 2003 (124
months). It begins within a few months of the inception of the arXiv, and thus
represents essentially the complete history of its ASTRO-PH section.
Dataset statistics
Nodes 18772
Edges 396160
Nodes in largest WCC 17903 (0.954)
Edges in largest WCC 394003 (0.995)
Nodes in largest SCC 17903 (0.954)
Edges in largest SCC 394003 (0.995)
Average clustering coefficient 0.6306
Number of triangles 1351441
Fraction of closed triangles 0.318
Diameter (longest shortest path) 14
90-percentile effective diameter 5.1
Source (citation)
J. Leskovec, J. Kleinberg and C. Faloutsos. Graph Evolution: Densification and
Shrinking Diameters. ACM Transactions on Knowledge Discovery from Data (ACM
TKDD), 1(1), 2007.
Files
File Description
ca-AstroPh.txt.gz Collaboration network of Arxiv Astro Physics category
| SVD-based statistics: | |
| norm(A) | 94.4415 |
| min(svd(A)) | 0 |
| cond(A) | Inf |
| rank(A) | 18,381 |
| null space dimension | 391 |
| full numerical rank? | no |
| singular value gap | 5.1072e+09 |
| singular values (MAT file): | click here |
| SVD method used: | s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero |
| status: | ok |
For a description of the statistics displayed above, click here.
Maintained by Tim Davis, last updated 12-Mar-2014.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.