A Primer on Graph-Theoretic Models and Metrics

As weapon systems become more complex, the need increases for mathematical tools to assess their robustness to random failures and attacks with the requisite rigor. The increasing digitization of engineering records in single, authoritative databases enables the use of more-sophisticated modeling tools. For nuclear programs, the need for improved assessment tools is most acute in the areas of nuclear certification, nuclear surety, and cybersecurity risk assessment.

This primer on graph theory provides tools to improve the rigor, reproducibility, and scalability of analytical tools that support cybersecurity assessment, nuclear surety, and nuclear safety certification. It is intended to help analysts use the power of graph theory to assess weapon systems and give those receiving such analysis a better context for understanding how to use the resultant insights.

The work summarizes the key areas of graph theory pertinent to nuclear certification, nuclear surety, and cybersecurity risk assessment. Much of the discussion is a summary of the literature, some of which contains quite recent discoveries. The authors combine the insights from the literature with their own experiences in modeling similar problems with graph theory and explain when a graph is a useful model of a system and when it is not.