Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks (1702.02246v2)

Abstract: We show that real multiplex networks are unexpectedly robust against targeted attacks on high degree nodes, and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

• The paper demonstrates that geometric correlations transform abrupt breakdowns into multistep cascading failures under targeted attacks.
• The study utilizes a two-layer multiplex model mapped to hyperbolic space to analyze both radial and angular correlations.
• Empirical results reveal that angular correlations significantly enhance network resilience, scaling the critical node threshold with system size.

Geometric Correlations in Multiplex Networks and Vulnerability Mitigation

The analysis of multiplex networks under targeted attacks is a crucial subject in understanding the robustness and vulnerability of interconnected systems. This paper addresses the impact of interlayer geometric correlations in multiplex networks, particularly examining how these correlations can mitigate the vulnerability of systems to targeted attacks on high-degree nodes.

Key Findings and Methodology

The paper demonstrates that real-world multiplex networks possess intrinsic robustness to targeted attacks, attributed to hidden interlayer geometric correlations. These correlations transform what would typically be a network's fragility into robustness against node failures. The research reveals that in the absence of geometric correlations, multiplex networks undergo abrupt breakdowns with respect to mutual connectivity, signifying discontinuous phase transitions. However, when geometric correlations are present, the networks exhibit a multistep cascading failure process, moving towards a continuous transition, particularly in the thermodynamic limit.

The authors employed a two-layer multiplex model and removed nodes sequentially based on their degree, recalculating the networks' structural integrity through the lens of mutual connectivity. A key feature of their analysis was mapping each network layer to a hyperbolic space, evaluating both radial (degree-based) and angular (similarity-based) correlations. Their findings indicated that angular correlations were significant in providing resilience against targeted attacks, more so than radial correlations.

Numerical Results and Implications

Various network datasets, including technological, biological, and social systems, demonstrated that real networks showcase a mitigated vulnerability due to hidden geometric correlations. The paper conducted a reshuffling of nodes to disrupt these correlations, revealing that reshuffled systems are drastically more susceptible to attacks, highlighting the importance of these geometric structures.

The empirical analysis provided a quantifiable measure of vulnerability and robustness through a metric called the critical number of nodes ($\Delta N$), indicating the points at which systems transition from robust to fragmented states. A significant finding was that $\Delta N$ scales with the system size if angular correlations are present, contrary to situations where they are absent. This observation confirms the hypothesis that angular correlations significantly enhance network resilience.

Implications for Network Design and Future Research

This investigation has both theoretical and practical implications for the design of robust multiplex networks. Practically, understanding and integrating geometric correlations into network design can improve the resilience of critical infrastructures against attacks or failures. Theoretically, it expands on the foundations of percolation theory by suggesting that geometric considerations should be integral to modeling efforts in the context of multiplex networks.

Future research could explore the detailed mechanisms through which geometric correlations arise in real-world systems and how these can be optimized for enhancing robustness further. Additionally, extending these findings to dynamic settings, where networks evolve over time, would provide a broader understanding of network resilience given the constantly changing nature of real-world systems.

In conclusion, the paper posits that geometric correlations are fundamental to the robustness of multiplex networks against targeted attacks, offering a new perspective on the interplay between network structure and resilience. These insights open new pathways for research and practical applications, particularly in designing more secure and robust systems in various domains.