# A New (aleph) Stochastic Quenched Disorder Model for Interaction of Network- Master node

## TL;DR

This paper introduces a stochastic model of a one-dimensional network with a master node influencing agents, revealing a phase transition from disorder to order and offering a framework for studying social phenomena like opinion formation and morality spread.

## Contribution

The paper presents a novel quenched disorder model incorporating a master node with preferential influence, advancing understanding of order-disorder transitions in social networks.

## Key findings

- Identified a phase transition from disorder to order in the model.
- Demonstrated the influence of the master node on network consensus.
- Proposed the model as a framework for social dynamics studies.

## Abstract

We consider a first neighbor interaction where agents are spread through a uni-dimensional network. Some agents are also connected to a hub, or master node, who has preferential values (or orientation). The role of master node is to persuade some individuals to follow a specific orientation, subject to a probability of successful persuasion. The connections between master node and the network society are quenched in disorder. Despite its simplicity, we found a phase transition from disorder to order for three different control parameters. We also discuss how this model may be useful as a framework to study the spread of morality, innovation, opinion formation and consensus. Is important to recall the route from disorder to order in social systems still a great challenge. We hope to contribute with a novel approach to model a this issues.