Theoretical exploration of network structure significance requires a range of different networks for comparison. Here, we present a new method to construct networks in a spatial setting that uses spectral methods in combination with a probability distribution function. Nearly all previous algorithms for network construction have assumed randomized distribution of links or a distribution dependent on the degree of the nodes. We relax those assumptions. Our algorithm is capable of creating spectral networks along a gradient from random to highly clustered or diverse networks. Number of nodes and link density are specified from start and the structure is tuned by three parameters (γ, σ, κ). The structure is measured by fragmentation, degree assortativity, clustering and group betweenness of the networks. The parameter γ regulates the aggregation in the spatial node pattern and σ and κ regulates the probability of link forming. Advs. Complex Syst. 2010.13:239-250. Downloaded from www.worldscientific.com by AUSTRALIAN NATIONAL UNIVERSITY on 03/16/15. For personal use only. 240 N. Hȧkansson et al. can be described and categorized according to different network measures [29].Statistics for a variety of empirical investigated networks can be found in [21].A well-studied group of networks are the random networks [3]. A random network is a graph with nodes randomly linked together. It means that a link between two nodes is completely independent of the presence of other links. Random graphs are frequently used in discrete mathematical problems but also in models of various real-world problems, especially epidemiological ones [22]. However, investigations of real-world networks show that their structure often is widely different from a random graph with Poisson distributed node degrees [22]. Thus, there is a great risk of missing important features if random graphs are used for network modeling. The concept of random graphs has therefore been developed to also include other degree distributions, for example exponential or power law distributions [28].Many real-world networks have been classified as scale-free networks or smallworld networks [4,30]. The method for classification of scale-free networks is however discussed and questioned [16]. In a scale-free network, the degree distribution of the nodes follows a power law. A common method of generating scale free graphs is by preferential attachment, that is networks are generated by attaching nodes at random to previously existing nodes with a probability proportional to the node degree [30]. A consequence of this method is a high proportion of disconnected graphs [1]. Uncorrelated scale-free networks can however be generated without preferential attachment by the uncorrelated configuration model (UCM) developed from the classical configuration models (CM) [9]. The CM models design network with an a priori set degree distribution and have also been developed to control degree-degree dependent correlations and/or degree dependent clustering [24,27,31].Some of the real-world...
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