Graph Analysis Using Fast Fourier Transform Applied on Grayscale Bitmap Images

Abstract

There is spiking interest in graph analysis, mainly sparked by social network analysis done for various purposes. With social network graphs often achieving very large size, there is a need for capable tools to perform such an analysis. In this article, we contribute to this area by presenting an original approach to calculating various graph morphisms, designed with overall performance and scalability as the primary concern. The proposed method generates a list of candidates for further analysis by first decomposing a complex network into a set of sub-graphs, transforming sub-graphs into intermediary structures, which are then used to generate grey-scaled bitmap images, and, eventually, performing image comparison using Fast Fourier Transform. The paper discusses the proof-of-concept implementation of the method and provides experimental results achieved on sub-graphs in different sizes randomly chosen from a reference dataset. Planned future developments and key considered areas of application are also described.

Quantum-Mechanical Modelling of Asymmetric Opinion Polarisation in Social Networks

“…Whereas the discussion above employs the terminology adopted in physics, we can establish a link between the physical concepts and those concepts used in data science and studies of social networks. Indeed, studies of social networks often exploit the notion of periodicity and rely on the Fourier transformation of data [93,94], highlighting the important role of the reciprocal space in analysis of big datasets [95,96]. Hence, readers who do not wish to use the physical language can also comprehend our model using the terminology adopted in the fields of graph signal processing [94], data science [93], or mathematical sociology [95].…”

“…Indeed, studies of social networks often exploit the notion of periodicity and rely on the Fourier transformation of data [93,94], highlighting the important role of the reciprocal space in analysis of big datasets [95,96]. Hence, readers who do not wish to use the physical language can also comprehend our model using the terminology adopted in the fields of graph signal processing [94], data science [93], or mathematical sociology [95]. Moreover, we present energy level plots alongside the dispersion diagrams, helping readers understand the mainstream discussion, without the need to use the concepts of wavevector and Brillouin zone.…”