An innovative approach to identifying rapidly spreading false information is to create a targeted graph and its subsequent clustering. A method for detecting rapidly spreading fake messages in social networks has been developed. K-means, Louvain, and Leiden algorithms were applied to identify large communities in graphs, enabling the rapid detection of fake news. A modified fake news detection algorithm based on k-means and Leiden can group fake news clusters, enabling rapid identification of widely spreading news. The combination of Leiden for structural analysis of communities and SVM for classification provides an optimal balance between accuracy (F1-score = 0.87) and completeness of fake detection (Recall = 97%), allowing the system to be used both for analysing large datasets and for monitoring new publications. The Lei-den algorithm demonstrated the highest modularity (Q = 0.7212), which is 4.8% better than Louvain (Q = 0.6884), and detected 40 structural communities. The modified method has a lower modularity (Q = 0.5584), since modularity is not calculated for K-means.

A method of identification of original and fake prints has been developed. Security elements are printed using an offset printing method, which we will call original printing. In parallel, we will print bitmap security elements on copiers. We will call this process fake printing. Such types of rasterisation were developed to make the difference between an original print and a fake print visible to the naked eye. A method of detecting fake printing has also been developed by measuring the change in the percentage of raster dot, dot gain, trapping, optical density, ∆lab, and change in tonality. The protection of the printed document is created when the image is transformed by amplitude-modulated rasterisation based on the mathematical apparatus of Ateb-functions. During rasterisation, we create thin graphic elements that have different shapes and are calculated according to developed methods. The size of a single dot of a raster element depends on the selection of the rasterisation method and the tonal gradation value of each corresponding pixel in the image. During rasterisation, a raster structure is formed, in which the value of each raster element is related by the value of the Ateb-function with tonal gradation, as well as a change in the angle, lines and shapes of the curves of a single raster. We offer raster image printing on various paper samples that are widely used today.