K-method of calculating the mutual influence of nodes in a directed weight complex networks

TL;DR

The paper introduces the K-method for calculating mutual influence in directed weight complex networks, utilizing Kirchhoff rules, and applies it to sparse networks with real-world concept nodes, defining new influence metrics.

Contribution

It proposes the K-method for influence calculation in complex networks, incorporating Kirchhoff rules, and introduces new influence metrics with semantic interpretation.

Findings

The K-method effectively measures mutual influence in directed networks.

New metrics 'pressure' and 'influence' provide semantic insights.

Applicable to sparse networks with real-world concepts.

Abstract

A new characteristic of paired nodes in a directed weight complex network is considered. A method (named as K-method) of the characteristics calculation for complex networks is proposed. The method is based on transforming the initial network with the subsequent application of the Kirchhoff rules. The scope of the method for sparse complex networks is proposed. The nodes of these complex networks are concepts of the real world, and the connections have a cause-effect character of the so-called "cognitive maps". Two new characteristics of concept nodes having a semantic interpretation are proposed, namely "pressure" and "influence" taking into account the influence of all nodes on each other.