Eigenvalue Spectra Measurements of Complex Networks

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.

• Type: Conference
• Year: 2008
• Where: CSC
• Authors: Kenneth A. Hawick
• Keywords: Applied Computing, Complex Networks, CSC 2008, Kauffman NK Model, Kauffman's NK Model