Computational Science Technical Note CSTN-051


Eigenvalue Spectra Measurements of Complex Networks

K. A. Hawick

Archived March 2008


Complex network models such as Kauffman's NK model have been shown to have interesting phase transitional properties as the connectivity is varied. Conventional network and graph analysis metrics concerning path-lengths, numbers of components and even circuits have been used to explore these transitions. This paper presents use of matrix analysis techniques to relate the shape and form of the eigenvalue spectrum of the adjacency matrices of complex networks to the phase transition. A number of computational experiments with different network realisations yield results for the Kauffman NK model at connectivity K = 1,2,...,7 are these are discussed in terms of the transition at K=2.

Keywords: complex networks; Kauffman network; eigenvalue densities; semi-circle rule.

Full Document Text: PDF version.

Citation Information: BiBTeX database for CSTN Notes.

BiBTeX reference:

  author = {K. A. Hawick},
  title = {Eigenvalue Spectra Measurements of Complex Networks},
  booktitle = {Proc. Int. Conf on Scientific Computing (CSC'08)},
  year = {2008},
  editor = {H.Arabnia},
  pages = {174-179},
  address = {Las Vegas},
  month = {14-17 July},
  publisher = {CSREA},
  institution = {Computer Science, Massey University},
  timestamp = {2008.03.27}

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