Towards Using DFT to Characterize Complex Networks

There are some Network Metrics that are very useful to analyze and model Complex Networks. These metrics, including the spectral-based ones, can be used to retrieve information from the network. As an example, the eigenvalues of the Laplacian matrix can present interesting information about the network topology. We observed that if one applies the Discrete Fourier Transform (DFT) over the eigenvalues of the Laplacian Matrix, it is possible to observe different patterns in the DFT depending on some properties of the analyzed networks. In this paper, we propose two novel metrics based on the DFT samples, named FZC and HVC, that can be used to identify the type of network. We tested these metrics in networks generated by three different models (Random, Small-World and Scale-free) and in real network benchmarks. The results indicate that one can use the proposed metrics to identify the generational model of the network.