Application of hypercomplex number system in the dynamic network model

TL;DR

This paper introduces a novel approach using hypercomplex number systems to model complex networks with multiple node properties, enabling more detailed analysis of mutual influences in dynamic networks.

Contribution

It proposes a new mathematical framework employing hypercomplex numbers to model multi-property nodes in complex networks, enhancing analysis capabilities.

Findings

Hypercomplex systems effectively model multi-property network nodes.

The Maple-based software facilitates complex network simulations.

The approach simplifies calculations through isomorphic transitions.

Abstract

In recent years, the direction of the study of networks in which connections correspond to the mutual influences of nodes has been developed. Many works have been devoted to the study of such complex networks, but most often they relate to the spread of one type of activity (influence). In the process of development of the newest technologies various mathematical models are developed and investigated: models with thresholds, models of independent cascades, models of distribution of epidemics, models of Markov processes. The paper proposes to use hypercomplex number systems, which are a mathematical apparatus that allows you to model some network problems and solve them at a new level, ie to consider a complex network with several properties in each node. In this paper, we consider networks where the edges correspond to the mutual influences of the nodes. It is proposed to match the number of properties in each node and the measurability of a hypercomplex number system(HNS) with the same number of basic elements. Each HNS corresponds to the Kelly table, which corresponds to the law of multiplication of these CSF. The properties of the CSF allow you to build an isomorphic transition from a filled Kelly table to a less filled one, which simplifies the calculation. To model the problem using hypercomplex number systems, we offer a specialized software package of hypercomplex computations based on the system of computer algebra Maple. All this made it easy to model a complex system with several effects.