SVD singular values does not decrease rapidly, but slowly

Question

[Eric Wang]

Hi all,

I used the svd() function (R language) to do SVD for the adjacency matrix of the protein-protein interaction network. However, the amount of information I get from singular values does not decrease rapidly, but slowly. I wonder why this is or is it reasonable?

For example:

The singular values from 1 to 100 are:

>   [1] 1.0074586 1.0070554 1.0063593 1.0059795 1.0055670 1.0053987 1.0051442
  [8] 1.0050790 1.0048908 1.0046617 1.0045478 1.0043112 1.0041319 1.0040420
 [15] 1.0039300 1.0035314 1.0033920 1.0033175 1.0032218 1.0029823 1.0028936
 [22] 1.0028239 1.0027816 1.0025896 1.0024478 1.0023495 1.0023147 1.0022161
 [29] 1.0021044 1.0019705 1.0018740 1.0017153 1.0016610 1.0015577 1.0014349
 [36] 1.0014156 1.0013212 1.0012127 1.0011715 1.0010235 1.0009524 1.0009048
 [43] 1.0008785 1.0008109 1.0007297 1.0006563 1.0005858 1.0005247 1.0004446
 [50] 1.0003866 1.0003573 1.0002762 1.0001141 1.0000404 0.9998874 0.9998039
 [57] 0.9997480 0.9997367 0.9995716 0.9995397 0.9994195 0.9993325 0.9992879
 [64] 0.9992163 0.9990943 0.9989908 0.9989651 0.9988125 0.9987165 0.9986866
 [71] 0.9986546 0.9985252 0.9983784 0.9982735 0.9981637 0.9980586 0.9978624
 [78] 0.9976935 0.9975900 0.9974132 0.9973097 0.9971579 0.9970841 0.9968607
 [85] 0.9966922 0.9965789 0.9964845 0.9962687 0.9960058 0.9958696 0.9955345
 [92] 0.9951622 0.9949442 0.9942553 0.9940109 0.9935174 0.9929589 0.9917055
 [99] 0.9903973 0.9802358

Best, Eric

[dariober]

Is the adjacency matrix a symmetric matrix of 0s and 1s?

[Eric Wang]

Yes, It is a binary matrix. To be precise, I use the Laplacian matrix of the adjacency matrix as the input of SVD.