umeyama.md
In iGraphMatch: Tools for Graph Matching

matching correspondence between graph1 and graph2

gm(A = A, B = B, seeds = seeds, similarity = startm, method = "Umeyama")

Match (10 x 10):
   corr_A corr_B
1       1      1
2       2      2
3       3      3
4       4      4
5       5      5
6       6     10
7       7      7
8       8      8
9       9      9
10     10      6

       [,1]   [,2]   [,3]   [,4]   [,5]   [,6]
[1,] 0.3343 0.4616 0.4806 0.3665 0.4122 0.3426
[2,] 0.4563 0.2167 0.2482 0.4459 0.2850 0.3560
[3,] 0.3591 0.0484 0.2007 0.4172 0.2271 0.1429
[4,] 0.3518 0.4352 0.4196 0.2497 0.2174 0.2887
[5,] 0.3377 0.1086 0.1573 0.2143 0.4112 0.0000
[6,] 0.3394 0.2550 0.3619 0.4142 0.3494 0.3950

matching correspondence between graph1 and graph2 for directed graphs

gm(A = A, B = B, seeds = seeds, similarity = startm, method = "Umeyama")

Match (10 x 10):
   corr_A corr_B
1       1      1
2       2      2
3       3      3
4       4      4
5       5      8
6       6      9
7       7      7
8       8     10
9       9      6
10     10      5

       [,1]   [,2]   [,3]   [,4]   [,5]   [,6]
[1,] 0.1611 0.0444 0.2043 0.1910 0.1604 0.1697
[2,] 0.1516 0.0230 0.2438 0.1733 0.1376 0.2431
[3,] 0.1771 0.1804 0.0420 0.1633 0.1506 0.0683
[4,] 0.1917 0.1640 0.1475 0.2369 0.1326 0.1431
[5,] 0.1436 0.0000 0.1973 0.1162 0.1116 0.2476
[6,] 0.2021 0.1388 0.1027 0.2275 0.2392 0.0682

Umeyama multi-layer

gm(A = A, B = B, seeds = seeds, method = "Umeyama")

Match (10 x 10):
   corr_A corr_B
1       1      1
2       2      2
3       3      3
4       4     10
5       5      5
6       6      7
7       7      8
8       8      4
9       9      9
10     10      6

       [,1]   [,2]   [,3]   [,4]   [,5]   [,6]   [,7]
[1,] 0.1489 0.2910 0.4429 0.5723 0.3430 0.4746 0.3901
[2,] 0.4582 0.3473 0.4220 0.4037 0.7949 0.5245 0.4643
[3,] 0.5459 0.5120 0.5900 0.3053 0.5080 0.4137 0.3767
[4,] 0.6006 0.6427 0.7308 0.5432 0.5847 0.6760 0.4930
[5,] 0.6498 0.2585 0.0000 0.4293 0.3338 0.4406 0.0450
[6,] 0.3963 0.6963 0.7036 0.3814 0.6653 0.3906 0.3809
[7,] 0.2398 0.1985 0.4464 0.6686 0.4418 0.5037 0.5102