Inter-similarity between coupled networks (1010.4506v1)

Abstract: Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of dependent nodes are coupled according to some regularity which we coin inter-similarity. For example, we study a system composed from an interdependent world wide port network and a world wide airport network and show that well connected ports tend to couple with well connected airports. We introduce two quantities for measuring the level of inter-similarity between networks (i) Inter degree-degree correlation (IDDC) (ii) Inter-clustering coefficient (ICC). We then show both by simulation models and by analyzing the port-airport system that as the networks become more inter-similar the system becomes significantly more robust to random failure.

• The paper introduces inter-similarity, showing that coupling high-degree nodes across networks measurably boosts system robustness.
• The paper proposes quantitative metrics—Inter Degree-Degree Correlation and Inter-Clustering Coefficient—to capture dependency regularities between networks.
• The results reveal that increased inter-similarity transforms failure transitions from abrupt to gradual, offering design insights for resilient infrastructure.

Inter-similarity Between Coupled Networks

The paper, "Inter-similarity between coupled networks," investigates the robustness of interdependent networks, particularly when the nodes are not randomly coupled. The authors introduce the concept of inter-similarity, where coupled nodes are linked based on certain regularities rather than randomly. The paper utilizes real-world networks, like worldwide port and airport networks, to demonstrate that inter-similarity can lead to enhanced robustness against random failures.

Key Contributions

1. Inter-similarity Concept: The paper introduces the notion of inter-similarity, which reflects the tendency of highly connected nodes in one network to be coupled with highly connected nodes in another network. This contrasts with the assumption of random dependency often used in previous models.
2. Quantitative Measures: Two metrics are proposed to quantify the inter-similarity between networks:
   • Inter Degree-Degree Correlation (IDDC): Measures the correlation of node degrees between coupled networks.
   • Inter-Clustering Coefficient (ICC): Evaluates how neighbors in one network link to neighbors in a coupled network.
3. Robustness Analysis: Through simulations, the authors show that as networks become more inter-similar, they display a significant improvement in robustness to random node failures. Additionally, the nature of network fragmentation transitions from a first-order to a second-order phase transition as inter-similarity increases.
4. Real-World Application: Examining port and airport networks, substantial inter-similarity (IDDC = 0.2) was found, which indicates that high-degree nodes in these networks tend to be coupled, underscoring the practical relevance of the inter-similarity concept.
5. Modeling Inter-similar Networks: A generalized Barabási-Albert model is proposed to generate inter-similar coupled networks, inherently incorporating inter-degree correlations without affecting the inter-clustering coefficient.

Implications and Future Directions

The findings imply several theoretical and practical implications:

• Theoretical Implication: The results highlight the importance of considering structured dependencies rather than random ones when analyzing interdependent networks. The identification of different phase transition behaviors underlines the complexity and richness of network behaviors not captured by simpler models.
• Practical Implication: The enhanced robustness associated with inter-similar dependencies has critical implications for designing resilient infrastructure networks. For instance, understanding inter-similarity can aid in structuring dependencies between power grids and communication networks to prevent cascading failures.
• Future Research: Future work can delve into the environmental and economic factors fostering inter-similar dependencies and extend the current models by including these dynamics. Additionally, exploring inter-similarity in networks with directed links or multi-layer interactions could yield further insights into complex system vulnerabilities and robustness.

In conclusion, this paper provides a comprehensive methodology for assessing and enhancing the robustness of complex interdependent systems. By introducing the notion of inter-similarity and providing concrete metrics to evaluate it, the paper lays the groundwork for future advancements in the design and analysis of resilient networked infrastructures.