Suppose I have a weighted adjacency matrix A representing a graph G. I use K-means on this matrix to group vertices together.

What is K-means finding exactly? I mean, what is the interpretation of the groups that I get out of running K-means on a weighted adjacency matrix?

Are these groups similar because the weights are similar?

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    $\begingroup$ What does it mean exactly, that you're "running k-means on a weighted adjacency matrix"? K-means typically operates on points in a vector space. Could you provide more detail about the exact procedure you're following and what your goal is? $\endgroup$ – user20160 May 28 '18 at 9:26
  • $\begingroup$ My goal is to group vertices according to affinity. I'm taking a graph, and extracting a weighted adjacency matrix A. Then I'm applying K-means on that matrix. In R you'd use kmeans(A). By doing this, vertices are grouped in k groups. I'd like to get an intuitive explanation of what these groups are. $\endgroup$ – mickkk May 28 '18 at 9:43
  • $\begingroup$ You don't use k-means on an adjacency matrix, not even a weighted one. K-means is meant to operate on the data matrix, because it needs to compute means. $\endgroup$ – Anony-Mousse Jun 4 '18 at 19:03

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