As the spectrum of k-values of the nodes increases, the network becomes more and more irregular and complex. However, in the general context of complex networks, it is defined in an abstract space with a set of nodes N = and a set of links connecting these nodes. A regular lattice where nodes are associated with fixed locations in space and each node connected to an equal number of nearest neighbours, is an example of a regular network. If an equal number of nodes can be reached in one step from all the nodes, the network is said to be regular or homogeneous. The number of nodes that can be reached from a reference node ı in one step is called its degree denoted by k i. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low-dimensional chaotic attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.Ī network is an abstract entity consisting of a certain number of nodes connected by links or edges. We numerically study the variation of heterogeneity for random graphs (as a function of p and N) and for SF networks with γ and N as variables. To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. The measure is applied to compute the heterogeneity of synthetic (both random and scale free (SF)) and real-world networks with its value normalized in the interval. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation.
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