## GAP/GAP-kron

GAP benchmark: kron
Name GAP-kron GAP 2855 134,217,726 134,217,726 4,223,264,644 4,223,264,644 Random Undirected Weighted Graph Yes 2017 S. Beamer, K. Asanovic, D. Patterson S. Beamer, K. Asanovic, D. Patterson
Structural Rank 71,164,263 0 100% 100% no no integer
Download ```GAP/GAP-kron matrix: this is the 'kron' graph from the GAP benchmark suite, as described in "The GAP Benchmark Suite", by Scott Beamer, Krste Asanovic', and David Patterson, https://arxiv.org/abs/1508.03619. In that paper, the Kron graph is described as follows: Kron (|V|=134.2M, |E|=2,111.6M, undirected) uses the Kronecker synthetic graph generator [19] with the same parameters as Graph 500 (A=0.57, B=C=0.19, D=0.05) [14]. It has been used frequently in research due to Graph 500, so it also provides continuity with prior work. [19] Jurij Leskovec, Deepayan Chakrabarti, Jon Kleinberg, and Christos Faloutsos. Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication. European Conference on Principles and Practice of Knowledge Discovery in Databases, 2005. [14] Graph500 benchmark. www.graph500.org. The matrix has been given random integer edge weights, in the range 1 to 255. The GAP breadth-first-search (BFS) benchmark generates 64 random source nodes and evaluates the time to compute the BFS from each of the 64 sources. The betweenness-centrality (BC) runs 16 trials with 4 source nodes each. These source nodes are the same, in the same order. That is, the first 4 BFS source nodes are the same 4 source nodes for the first trial of BC. In ONE-based notation (where nodes are numbered 1 to n), the 64 source nodes are: 2338013 31997660 23590941 43400605 75337938 169868 104041221 94177943 32871358 56230003 69883038 9346346 48915359 122571174 6183280 86323664 106725781 92389939 16210739 59816701 111669930 102831412 113384801 43872565 80508828 26105649 8807517 118452456 121818860 42361929 29493054 98461504 71931338 103808469 4092346 115276242 4649344 76656190 31312002 111334128 100962919 41823216 22631241 42848462 79485149 106818743 73347975 78848446 109920511 121492134 101037297 15438601 4584785 124503846 87241744 108297009 33955083 79934824 8608482 82435064 46579272 515422 121530468 127978737 The first row are the 4 source nodes for the first BC trial, the 2nd row is for the second BC trial, and so on. These node ids also appear as Problem.aux.sources, in one-based notation. One-based notation is used because the Matrix Market format is one-based, as is MATLAB. If you use a zero-based method (such as the GAP benchmark itself, or the C API to GraphBLAS), be sure to subtract one from the node ids above (and in Problem.aux.sources) to obtain the right source nodes. The GAP/GAP-kron matrix was generated by the GAP benchmark and then incorporated into the SuiteSparse Matrix Collection by Tim Davis.```