# A new design principle of robust onion-like networks self-organized in growth

## TL;DR

This paper proposes a new network design principle that enhances robustness by self-organizing through the growth of interwoven long loops, improving resilience without sacrificing efficiency.

## Contribution

It introduces a novel incremental growth method for networks that increases robustness via loop enhancement, applicable even to vulnerable real-world networks.

## Key findings

- Networks grown with the new principle show high robustness against attacks.
- The method maintains path efficiency during growth.
- Connectivity tolerance can be improved in existing vulnerable networks.

## Abstract

Today's economy, production activity, and our life are sustained by social and technological network infrastructures, while new threats of network attacks by destructing loops have been found recently in network science. We inversely take into account the weakness, and propose a new design principle for incrementally growing robust networks. The networks are self-organized by enhancing interwoven long loops. In particular, we consider the range-limited approximation of linking by intermediations in a few hops, and show the strong robustness in the growth without degrading efficiency of paths. Moreover, we demonstrate that the tolerance of connectivity is reformable even from extremely vulnerable real networks according to our proposed growing process with some investment. These results may indicate a prospective direction to the future growth of our network infrastructures.