DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS

The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres [Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile, Potential Anal. 30(1) (2009) 1–27] as a tool to study internal diffusion limited aggregation. In this work, we investigate the shape of the divisible sandpile model on the graphical Sierpinski gasket [Formula: see text]. We show that the shape is a ball in the graph metric of [Formula: see text]. Moreover, we give an exact representation of the odometer function of the divisible sandpile.

Application of Graph Analytics for Simulations of Electronic Money Turnover: Solutions, Evaluations, Forecasts

The graph model for electronic money turnover developed in this paper considers the system of electronic money turnover as a technological complex network. This network includes systems of electronic money payments, communications between bank and its clients, and interbank communications. The application of the graph models is based on its essential advantages such as an opportunity to expand this system to arbitrary size and visualization of the system links. While graph plotting provides us with the opportunity of carrying out qualitative (visual) system analysis, e computations of the graph metric allows performing a more quantitative analysis. The composite metric, created on the base of graph centrality measures and giving us possibilities of estimating and ranking potential risks, is considered as a foundation for methods of stability, quality and economic security control for systems of the electronic money turnover. A validity of this classification has been investigated and supported by the so-called crash tests, which simulate the random consecutive deleting of graph nodes represented in the real life by communication network nodes, for example, banks or other members of electronic money turnover system, and also by the analysis of the overall performance of the system.