Hidden multiscale organization and robustness of real multiplex networks

Area of Science:

• Network science
• Complex systems analysis
• Graph theory

Background:

• Hidden geometry provides a framework for analyzing complex networks across scales.
• Multiplex networks consist of multiple interconnected layers, presenting unique organizational challenges.
• Understanding mesoscopic organization is crucial for network resilience.

Purpose of the Study:

• To extend the hidden geometry framework to multiplex networks.
• To identify and characterize novel mesoscopic structures within multiplex systems.
• To investigate the relationship between network structure, robustness, and vulnerability.

Main Methods:

• Application of hidden geometry principles to multiplex network analysis.
• Identification of 'clan' structures—groups of nodes preserving local geometry across layers.
• Analysis of mutual percolation dynamics under targeted attacks.
• Correlation analysis between geometric organization and system robustness.

Main Results:

• Discovery of 'clan' as a new mesoscopic organization in multiplex networks.
• Clans exhibit preserved local geometric arrangements across network layers.
• Clan structure influences mutual percolation, creating an ambivalent role in system stability.
• Multiscale geometric organization correlates with overall network robustness.

Conclusions:

• Hidden geometry is significant for understanding multiplex network function and organization.
• Clans introduce fragility but also resilience against catastrophic failure in multiplex systems.
• The multiscale nature of geometric organization is key to network robustness.
• Findings offer insights into evaluating and mitigating failures in complex multiplex systems.