# Influence and Betweenness in Flow Models of Complex Network Systems

## TL;DR

This paper introduces new measures of influence and betweenness in flow models of complex networks, providing quantitative tools to assess node and subsystem importance in network dynamics and robustness.

## Contribution

It develops novel influence and betweenness metrics based on flow adjacency matrices for analyzing the functional importance of nodes and subsystems in complex networks.

## Key findings

- Quantitative measures of influence and betweenness for nodes and edges.
- Application of these measures to real complex network systems.
- Insights into network robustness and vulnerability.

## Abstract

This paper provides the analysis for functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced. The concepts of strength, power, domain and diameter of influence of complex network nodes are analyzed for the purpose of determining their importance in the systems structure. The notions of measure, power, domain and diameter of betweenness of network nodes and edges are introduced to identify their significance in the operation process of network systems. These indicators quantitatively express the contribution of the corresponding element for the motion of flows in the system and determine the losses that are expected in the case of blocking this node or edge or targeted attack on it. Similar notions of influence and betweenness are introduced to determine the functional importance of separate subsystems of network system and the system as a whole. Examples of practical use of the obtained results during investigation of real complex network systems are given.

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Source: https://tomesphere.com/paper/1907.10667