Spectral Analysis of Growing Graphs

A Quantum Probability Point of View

  • NobuakiĀ Obata

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 20)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Nobuaki Obata
    Pages 1-15
  3. Nobuaki Obata
    Pages 17-29
  4. Nobuaki Obata
    Pages 31-41
  5. Nobuaki Obata
    Pages 43-61
  6. Nobuaki Obata
    Pages 63-77
  7. Nobuaki Obata
    Pages 79-99
  8. Nobuaki Obata
    Pages 101-128
  9. Back Matter
    Pages 129-138

About this book


This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs.
This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.


quantum probability graph spectra complex networks orthogonal polynomials asymptotic combinatorics

Authors and affiliations

  • NobuakiĀ Obata
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

Bibliographic information