Spectral analysis of community structure in complex networks: a case study of book-borrowing networks

• Main Authors: Cing-De Gong, 龔清德
• Other Authors: Chi-Ning Chen
• Format: Others
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/3w93p7

碩士 === 國立東華大學 === 物理學系 === 100 === In this study, we use book-borrowing records of National Dong-Hua university library between January 2009 to June 2012 to build a real social network which contains 13,241 nodes, i.e. readers. The degree distribution of this book-borrowing network is a exponential decay function. Its short average path length(1.93) and high clustering coefficient(0.34) indicate the small-world feature. We go further to pick up two to three departments to build a small detailed book-borrowing network. Based on the number of the same books borrowed, we construct a similarity matrix to represent the relationship between nodes. By diagonalizing and analysing its eigenvalues and eigenvectors, we may probe the community structure in the book-borrowing network.