# Emergent Network Modularity

## TL;DR

This paper presents a new network growth model based on complete redirection, resulting in highly modular networks with macrohubs and a small core, revealing unique structural properties of emergent network modularity.

## Contribution

The paper introduces a novel network growth mechanism that produces highly modular networks with macrohubs and a small core, advancing understanding of network structure formation.

## Key findings

- Networks exhibit multiple macrohubs with degree scaling linearly with N.
- The network's nucleus grows sublinearly, becoming negligible as N increases.
- Networks are predominantly leaves with a tiny core as size grows large.

## Abstract

We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual, highly modular networks. Individual network realizations typically contain multiple macrohubs---nodes whose degree scales linearly with the number of nodes $N$. The size of the network "nucleus"---the set of nodes of degree greater than one---grows sublinearly with $N$ and thus constitutes a vanishingly small fraction of the network. The network therefore consists almost entirely of leaves (nodes of degree one) as $N\to\infty$.