Assortativity in cyber-physical networks

Many complex systems are amenable to be described as networks (Solé and Valverde, 2004; Albert and Barabasi, 2002; Albert et al., 1999; Newman, 2003), and it has been a recent trend to study common topological features of such networks. Network diameter, clustering coefficients, modularity, community structure, information content are some features analysed in recent literature (Alon, 2007; Lizier et al., 2009; Piraveenan et al., 2009a; Prokopenko et al., 2009). One such measure that has been analysed extensively is assortativity (Newman, 2002; Albert and Barabasi, 2002; Newman, 2003; Callaway et al., 2001). Having originated in ecological and epidemiological literature (Albert and Barabasi, 2002), the term ‘assortativity’ refers to the correlation between the properties of adjacent network nodes. Based on degree-degree correlations, assortativity has been defined as a correlation function: the networks that have a positive correlation coefficient are called assortative; while the networks characterised by a negative correlation coefficient are called disassortative. The precise local contribution of each node to the global level of assortative mixing — “local assortativity” — can also be quantified (Piraveenan et al., 2008, 2009b, 2010). Local assortativity profiles (as distributions of local assortativity over nodes’ degrees) may be constructed for various networks, and used to classify cyber-physical networks (Piraveenan et al., 2008). In this paper, our objective is to characterise classes of networks in terms of the unbiased formulation of local assortativity (Piraveenan et al., 2010).