Hi

I am interested in generating adjacency matrices using k-nearest networks approach. I have couple of questions regarding this .

1) Assuming the embedding dimension is m, i will get m-1 adjacency matrices ( for dimension 2 to m ). I am interesting in computing some network measures like clustering coefficient. Do I compute this measure for each dimension and then average it ? Or how do it take all the dimension into consideration while finding k-nearest neighbors for each observation vector ?

2) k-nearest neighbor approach gives asymmetric matix that is directed. I know i can obtain undirected network by artificially making it symmetric such that if r(i,j) = 1, make r(j,i) = 1 (Shimada et al. 2008). But is such an approach good ? Does it not change the network structure by introducing links which did not exist in the first place according to the 'nearest neighbors' condition ? So is it then better to derive measures for directed, asymmetric graph ?

Please note that I am trying to derive these measures for one channel EEG signal.

Thank You