#### Computational Science Technical Note CSTN-051

#
Eigenvalue Spectra Measurements of Complex Networks

##
K. A. Hawick

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Archived March 2008

**Abstract**

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:**

@INPROCEEDINGS{CSTN-051,
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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