What is the interpretation of K-means clustering on a weighted adjacency matrix?

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?

• 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? – user20160 May 28 '18 at 9:26
• 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. – mickkk May 28 '18 at 9:43
• 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. – Anony-Mousse Jun 4 '18 at 19:03