Abstract:Consider a network where the nodes split into $K$ different communities. The
community labels for the nodes are unknown and it is of major interest to
estimate them (i.e., community detection). Degree Corrected Block Model (DCBM)
is a popular network model. How to detect communities with the DCBM is an
interesting problem, where the main challenge lies in the degree heterogeneity.
We propose a new approach to community detection which we call the Spectral
Clustering On Ratios-of-Eigenvectors (SCORE). Co ...
Why does it suffice to apply some clustering algorithm such as K-means or Hierarchical clustering to the matrix of eigenvalue ratios in order to detect communities? That is, why is it that looking at the matrix of the eigenvalue ratios organizes the community data so that ordinary clustering methods can accurately detect the community structure?