The Algorithm of Accumulated Mutual Influence of The Vertices in Semantic Networks

TL;DR

This paper introduces a new algorithm for calculating mutual influence in cognitive maps that overcomes limitations of the impulse method, providing stable, scale-invariant results regardless of initial impulses or graph stability.

Contribution

The paper presents a novel algorithm for mutual influence calculation in semantic networks that is stable, scale-invariant, and independent of initial impulses, unlike existing methods.

Findings

The algorithm always produces results regardless of graph stability.

Results are unaffected by initial impulse values.

The algorithm maintains scale invariance when increasing matrix elements.

Abstract

In this article the algorithm for calculating a mutual influence of the vertices in cognitive maps is introduced. It has been shown, that in the proposed algorithm, there is no problem in comparing with a widely used method - the impulse method, as the proposed algorithm always gives a result regardless of whether impulse process, which corresponds to the weighted directed graph, is a stable or not. Also the result of calculation according to the proposed algorithm does not depend on the initial impulse, and vice versa the initial values of the weights of the vertices influence on the result of calculation. Unlike the impulse method, the proposed algorithm for calculating a mutual influence of the vertices does not violate the scale invariance after increasing the elements of the adjacent matrix, which corresponds to the cognitive map, in the same value. Also in this article the advantages of the proposed algorithm on numerous examples of analysis of cognitive maps are presented.