Model of communities isolation at hierarchical modular networks

TL;DR

This paper extends a community isolation model to hierarchical modular networks, showing how blocked nodes grow over time and analyzing the distribution of first isolated clusters with analytical and simulation agreement.

Contribution

It introduces a model of community isolation on hierarchical modular networks and provides analytical insights into the dynamics of node blocking and cluster formation.

Findings

Blocked nodes increase as a power function over time.

Distribution of first isolated cluster times is unimodal and non-Gaussian.

Analytical results align well with simulations.

Abstract

The model of community isolation was extended to the case when individuals are randomly placed at nodes of hierarchical modular networks. It was shown that the average number of blocked nodes (individuals) increases in time as a power function, with the exponent depending on network parameters. The distribution of time when the first isolated cluster appears is unimodal, non-gaussian. The developed analytical approach is in a good agreement with the simulation data.