
TL;DR
The paper introduces SCORE, a spectral clustering method that uses entry-wise ratios of eigenvectors to effectively detect communities in networks with degree heterogeneity, outperforming classical spectral and modularity methods.
Contribution
SCORE is a novel spectral clustering approach that removes degree heterogeneity effects via eigenvector ratios, improving community detection accuracy and computational efficiency.
Findings
SCORE achieves lower error rates than classical spectral methods.
SCORE is easier to implement and faster than modularity methods.
Theoretical analysis confirms SCORE's consistency under mild conditions.
Abstract
Consider a network where the nodes split into 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). Compared to classical spectral methods, the main innovation is to use the entry-wise ratios between the first leading eigenvector and each of the other leading eigenvectors for clustering. Let be the adjacency matrix of the network. We first obtain the leading eigenvectors of , say, , and let be the matrix such that…
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