Abstract: This article attempts to broaden the modern representations on criminal environment existing in the conditions of globalization and digitalization of virtually all spheres of human and social life. Special attention is paid to the reference frame of current criminal activities. The authors examine the conditions and factors associated with extensive development and proliferation of information technologies and accompanying the emergence, advancement and self-organization of criminality. Positive foreign experience in the area of counteracting cyber threats and criminalization of cyberspace is reviewed. The authors lean on the achievements of Soviet criminology and scientific representations of the criminal environment. Systematization and generalization of the traditional criminological perceptions on criminal activities in light of the current trends in the area of total informatization of the society allow describing and getting deeper understanding of the essence and structure of modern criminality on the new methodological level. This in turn, creates theoretical and methodological platform for the development of measures on counteracting criminal cyber threats.   

Abstract: The object of the research are certain analytical tasks that arise before the subjects of the investigation of crimes related to the establishment of interrelations between the defendants of the crime and the circumstances of its commission, such as date, time, place, etc. The subject of the study is a formal formulation of these problems, based on elements of graph theory. Hypothetically, the received formal notations of analytical problems will allow to increase the level of automation of analytical work on the investigation of crimes. The author pays attention to the issues of mapping the data available to the analyst as a graph with subsequent formalization of the facts to be ascertained. The research methodology consists of the fundamentals of graph theory, elements of matrix theory, as well as general scientific methods of analysis and synthesis. The main results of the study are formalized statements of analytical problems arising during the investigation of crimes, such as: the establishment among the members of the organization of the person with the greatest number of contacts; the identification of the person connected with the greatest number of circumstances; the establishment of an indirect link between persons through available information on the circumstances of the crimes committed.

Abstract: The study is devoted to the influence (centrality) model of a social network participant.  The object of studies involves calculations for the centrality metrics, which are based upon the shortest path lengths between the graph vertices for the social graph based upon the iterative performance of the Flajolet-Martin algorithm. The author evaluates the possibility of approximateå evaluation of closeness-centrality based on a simple example. Then, having the calculation results, teh author compares the computed values with the real closeness values, as computed by breadth-first search algorithm (BFS-Algorithm). The methodology of the study involves graph theory elements, as well as the social network analysis apparatus, which allows to compute different centrality metrics of a graph vertex. The key conclusion provides that the Flajolet-Martin algorithm is an easily adaptable tool for the approximate social graph vertex centrality evaluation related with the shortest paths, such as closeness or centrality of the disintegration, as provided for in the work so M. Jackson. In turn, it provides for the new possibilities for the process modeling for the spread of information in the social networks.

Abstract: The object of studies concerns the methods for evaluation of the graph nodes. The author pays attention to the fact that the existing centrality metrics, such as level centrality, closeness centrality, interval centrality, own vector, etc., are sometimes not suitable for modeling the situations, when graph nodes are social object models, and therefore, they are capable of cooperation in order to achieve social goals.  In this case game-theoretic centrality models (such as coalition games models) are better suited to reflect the modeling object.  The methodology of the study involves the elements of graph theory, probability theory, as well as the apparatus for the analysis of social networks as a new independent scientific sphere. The key result of the stuy is that game-theoretic centrality based upon the Shapley vector is a flexible and mostly universal instrument for the social graph analysis.  It allows to consider an unlimited set of quality characteristics of the graph nodes, as well as their topological qualities in any combination in order to evaluate the nodes.

Abstract: The article focuses on the modeling of information dissemination in online social networks through reposts. The author considers the threshold model and an independent cascade model of information spreading in network. In the context of the independent cascade model author suggests a method of estimating the probability of spreading of information for each pair of connected users. The article reviews visible activity of online social network users that affect the likelihood for a particular user to read the information message, published by one of his friends, and then make a repost. The methodology of the study is related to the mathematical modeling of social processes. To build the model the author uses elements of set theory, graph theory. The main conclusion is that of the models considered (the threshold model and the independent cascade model), which both are special cases of same generalized model, it is the independent cascade model that most accurately reflects the logic of the process of information spreading in the online social network via reposts. The scientific novelty of the work lies in the fact that using the results for independent cascade model the author provides a method for the evaluation of information transmission probabilities for each pair of connected users.