K-core robustness in ecological and financial networks

Area of Science:

• Network Science
• Complex Systems Analysis
• Ecological and Financial Modeling

Background:

• Real-world networks (e.g., financial, ecological) require robustness against attacks, extinctions, and shocks for system survival.
• Previous robustness assessments relied on metrics like nestedness and degree distribution.
• Understanding network resilience is vital for dependent structures like economies and ecosystems.

Purpose of the Study:

• To introduce a novel method for characterizing network stability and robustness using k-shell distribution.
• To analyze networks with all-positive interactions.
• To identify structural properties that confer resilience.

Main Methods:

• Analysis of k-shell occupancy distribution in financial and ecological networks.
• Characterization of network structure through k-shell decomposition.
• Comparative analysis of network properties and resilience.

Main Results:

• A "U-shaped" k-shell occupancy histogram (high occupancy in inner/outer shells, low in middle shells) signifies resilience to targeted and global attacks.
• This structure was observed in both financial and ecological networks.
• The k-shell analysis revealed significant structural shifts in financial networks and provides a basis for predicting ecosystem stability.

Conclusions:

• The "U-shaped" k-shell occupancy distribution is a key indicator of network robustness and stability.
• This finding offers a universal metric for network health across diverse systems, including financial markets, ecosystems, and potentially internet and opinion networks.
• Monitoring k-shell composition allows for prediction of network transitions and vulnerabilities.