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The Dyadic Curvelet Transform for Multiscale Topological Complex Networks

The Dyadic curvelet transform (DClet), a newly proposed extended curvelet transform to generate the multiscale non-redundant transformation, is proposed for understanding the topology of complex networks. Because of the essence of the DClet that decomposes an input into coefficients and investigates them individually in different levels, it is proposed for deriving topology of complex networks. The proposed construction behaves the same matter as human eyes, processing an object by filtering the input data into a number of bands and levels. It is tested on telecommunication network of Iran as a real extremely complex network with 92 intercity switching nodes, 3600 transmission nodes with 706350 E1 traffic channels and 315525 transmission channels. It is shown the properties of small world and scale free phenomena in telecommunication network and it is represented how the properties of the intercity network can be derived from the DClet decomposition. The simulation results exhibit that the new approach can be considered as a simulation tool for successfully design of the network topology and establishing the necessary trunk group sizes