IEICE Information and Communication Technology Forum
Experimental Study on Relationship between Indices of Network Structure and Spectral Distribution of Graphs
Ryosuke Sawada, Yusuke Sakumoto, Chisa Takano, Masaki Aida,
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Spectral graph theory uses the Laplacian matrix of a network to analyze its network structure.The Laplacian matrix is defined by node degrees and adjacency relationships between nodes.A previous study clarified that the eigenvalue distribution of the Laplacian matrix has a high similarity to the distribution of node degrees used in the Laplacian matrix.Degree distribution does not contain the information of adjacency relationships between nodes, so the previous study did not clarify the effect of the adjacency relationship information on the eigenvalue distribution of a Laplacian matrix. In this paper, for understanding such an effect, we investigate the relationship between the eigenvalues of the Laplacian matrix and the familiar indices (i.e., average path length and clustering coefficient), which are affected with adjacency relationship information.