Assortativity Decreases the Robustness of Interdependent Networks (1203.0029v2)

Abstract: It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e. the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture, and thus enhances the level of protection of critical infrastructures.

• The paper finds that assortativity in interdependent networks significantly reduces robustness by lowering the critical threshold for failure propagation.
• The study demonstrates that scale-free (SF) networks are significantly more fragile than Erdős-Rényi (ER) networks as assortativity increases.
• The analysis reveals a first-order phase transition for failure propagation and suggests designing less assortative interdependent networks to increase robustness.

Assortativity Decreases the Robustness of Interdependent Networks

The paper "Assortativity Decreases the Robustness of Interdependent Networks" by Di Zhou et al. examines the influence of assortativity on the robustness of interdependent networks specifically within a model consisting of two interconnected networks. Through computational simulations, the authors explore how node correlations impact failure propagation and percolation transitions. The paper notably contrasts the impact of assortativity on Erdős-Rényi (ER) and scale-free (SF) networks within this context, indicating that SF networks are particularly vulnerable to increased assortativity.

Core Findings

1. Assortativity and Percolation Transition: Assortativity within the interdependent network system significantly reduces robustness by lowering the critical density of failures required to disrupt connectivity. In high assortative networks, nodes with similar degrees tend to be connected, exacerbating vulnerability under cascading failures.
2. Comparison of Network Types: The paper contrasts ER and SF networks, demonstrating that SF networks exhibit marked fragility with increasing assortativity. This observation correlates with previous findings about the general resilience of different network structures, noting that ER networks are less affected by variations in assortativity.
3. Phase Transition Order: Through simulations, the analysis reveals that the phase transition associated with failure propagation in these interdependent networks is first-order. This determination is made by observing the fluctuation profiles in the network under stress conditions.

Methodological Approach

The authors employ a model of interacting failure (IFM) to simulate cascading faults within the two-network system. The network configurations are generated using Monte Carlo (MC) methods with a rewiring process that varies assortativity while maintaining a fixed degree distribution. This approach allows the precise measurement of how assortativity affects network robustness under stress.

Implications

The implications of this research are pertinent to the understanding and design of critical infrastructures where interdependent network models are applicable. Assortativity, which may intuitively seem beneficial due to enhanced connectivity among similar nodes, actually heightens systemic fragility in interdependent settings. The findings suggest that strategies to mitigate vulnerability might include designing network topologies that are less assortative to limit cascading disruptions.

Future Directions

The research opens avenues for further exploration into the interplay between network topology and robustness, particularly in applications to real-world systems like power grids and communication networks. Subsequent studies could delve into dynamic changes in assortativity as a response to stress and the potential adaptive measures that interdependent systems might inherently employ to mitigate risk.

Understanding the effects of network topology in interdependent systems is critical, especially as systems become increasingly complex and interconnected. Identifying configurations that optimize robustness without sacrificing functionality could guide the development of more resilient infrastructures in the future. Furthermore, expanding the work to incorporate other types of networks and real-world data could enhance the applicability of the findings.