Visualization of Complex Networks Based on Dyadic Curvelet Transform

A visualization method is proposed for understanding the structure of complex networks based on an extended Curvelet transform named Dyadic Curvelet Transform (DClet). The proposed visualization method comes to answer specific questions about structures of complex networks by mapping data into orthogonal localized events with a directional component via the Cartesian sampling sets of detail coefficients. It behaves in the same matter as human visual system, seeing in terms of segments and distinguishing them by scale and orientation. Compressing the network is another fact. The performance of the proposed method is evaluated by two different networks with structural properties of small world networks with N = 16 vertices, and a globally coupled network with size N = 1024 and 523 776 edges. As the most large scale real networks are not fully connected, it is tested on the telecommunication network of Iran as a real extremely complex network with 92 intercity switching vertices, 706 350 E1 traffic channels and 315 525 transmission channels. It is shown that the proposed method performs as a simulation tool for successfully design of network and establishing the necessary group sizes. It can clue the network designer in on all structural properties that network has.