Semilocalization for inhomogeneous random graphs

Key Points

• Eigenvectors associated with the greatest eigenvalues primarily support high-degree vertices, enhancing understanding of graph structure.
• The greatest eigenvalues played a crucial role, indicating a correlation with vertex degree.
• Analysis of the adjacency matrix within the generalized random graph model provided essential insights into graph behavior.
• The findings imply that higher degree vertices significantly influence the spectral properties of random graphs.

Abstract