Optimal cost for strengthening or destroying a given network

Area of Science:

• Network Science
• Complex Systems Analysis
• Graph Theory

Background:

• Network resilience and vulnerability are critical in diverse applications, from infrastructure design to disease control.
• Understanding node importance based on connectivity is key to efficient network manipulation.
• Existing methods often lack a cost-optimization framework for targeted node interventions.

Purpose of the Study:

• To develop a universally applicable, cost-minimal method for strengthening or destroying random networks.
• To identify a degree-based priority list for node selection in network interventions.
• To analyze the impact of node cost-degree correlation on network manipulation strategies.

Main Methods:

• Defining a cost function c(k) based on node degree k.
• Developing a degree-priority list derived from the cost function.
• Applying the priority list to select nodes for strengthening or destruction to minimize total cost.
• Analyzing the universality of the priority list across different random network types.

Main Results:

• A universal, degree-based priority list for node strengthening or destruction was identified.
• This priority list is independent of the network's specific degree distribution.
• The optimal strategy for minimum cost strengthening or destruction is consistent across various random networks.
• A difference in the critical fraction of nodes (p_c) for giant component existence was observed between strengthening and destruction.

Conclusions:

• The developed method provides an efficient, cost-minimal approach to network strengthening and destruction.
• The universality of the degree-priority list simplifies network intervention strategies.
• While the node selection priority is similar for strengthening and destruction, the network's robustness (p_c) differs, highlighting distinct implications for resilience and vulnerability.