Topological structure of computing clusters description method based on operations of subgraphs multiplication

Topological structure of communication networks in supercomputers with grow in size and complexity of installation, respectively becomes more difficult. There are many methods to describe it, but such descriptions are cumbersome, which makes them difficult to manipulate. The article proposes an approach to describing the communication environment of a supercomputer, when the communication network is described as a constructor. The elements of the constructor are typical topological structures often found in various computing systems. For this purpose, a language for describing the topological structure has been developed. It based on the operation products of subgraphs. The language is ideologically similar in its principles to the NetML and OMNeT++ languages. Special attention is paid to exceptions in the regularity of networks of real supercomputers; in order to add the possibility of describing this fact, special constructions have been introduced into the language. A library has been developed in the C programming language with purpose to facilitate work with the language intoduced in this article. Also a special wrapper over C library has been written in Python3, which then can be used to visualize graphs described by the language. The expressive power of language has been demonstrated in the description computing clusters: Tianhe-2A, AI Bridging Cloud Infrastructure and Lomonosov-2. The method has been tested and compared with GraphViz DOT it is showed multiple reductions in the Record volume required to save topology for some of the major Top500 systems.