Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs

TL;DR

This paper introduces Mandala Networks, a novel network design that achieves complete robustness against failures and attacks, while maintaining ultra-small-world properties and high sparsity, optimizing security, efficiency, and cost-effectiveness.

Contribution

It presents a systematic method to construct scale-free networks that are fully robust, ultra-small-world, and highly sparse, addressing security and economic demands.

Findings

Networks are 100% robust against failures and attacks.

As networks grow, shortest paths stabilize, and link density approaches zero.

Networks are both ultra-small-world and highly sparse.

Abstract

The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are 100$\%$ robust against random failures as well as to malicious attacks. Furthermore, as the sizes of these networks increase, their shortest paths become asymptotically invariant and densities of links go to zero, making them ultra-small worlds and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically.