Application of Spectral Clustering Methods in Pipeline Systems Graph Models

Abstract

Among the many tasks on graphs, studies related to partitioning an initial graph into a predetermined number of connected disjoint components have found wide practical application -graph clustering, for example, is used in computer networks, transport, pattern recognition, and in many other areas. The decomposition methods of graph structures make a significant contribution to the performance of search algorithms, which is especially important in the context of restrictions on computing and time resources. And here we should pay special attention to the class of spectral clustering methods that combine elements of graph theory and linear algebra. In this paper, we consider the basic principles of the theory of spectral clustering, describe the main approach of normalized spectral clustering of graphs. Decomposition of any graph as a structure with inherent topology meets the criteria for optimality in connectedness and balanced subgraphs with a small number of clusters. With an increase in the number of sub-areas above a certain value, the probability of appearance of the disconnected subgraphs in the decomposition structure increases. To solve this problem, the authors propose an algorithm for the priority distribution of nodes based on iterative transfer of nodes of isolated areas to the most priority neighboring subgraphs. It is considered the question of optimal placement of objects in graph models of hydraulic networks by methods based on trial and error algorithms, greedy and spectral clustering.