Using effective graph resistance as a robustness metric

Abstract

This presentation addresses the quantification and improvement of network robustness using graph‑theoretical metrics, with a particular focus on effective graph resistance (RG). It reviews foundational concepts such as degree distributions, shortest paths, adjacency and Laplacian spectra, and illustrates how spectral properties relate to vulnerability assessment. RG is introduced as a comprehensive robustness metric that incorporates all paths between nodes and connects directly to the Laplacian eigenvalues. The method is applied to power grids, demonstrating how RG correlates with cascading‑failure vulnerability and how analytical metrics complement simulation‑based approaches. Finally, the talk examines optimisation strategies—such as 1‑GRIP and k‑GRIP—for enhancing robustness through targeted link additions, supported by heuristic and stochastic algorithms, and outlines directions for future research on spectral bounds, algorithmic performance, and interdependent infrastructures.

Biography

Robert Kooij has a background in mathematics: he received both his MSc and PhD degree cum laude at Delft University of Technology, in 1988 and 1993, respectively. From 1997 until 2003 he was employed at the research lab of KPN, the largest telecom operator in the Netherlands. From 2003 until 2018 he was employed at the ICT Unit of TNO, the Netherlands Organization of Applied Scientific Research. In 2011 he became principal scientist, conducting and managing research on Critical ICT Infrastructures. Since 2005 Robert is part-time affiliated with the Delft University of Technology, at the faculty of Electrical Engineering, Mathematics and Computer Science. Since 2010 he is a part-time full professor with the chair “Robustness of Complex Networks”. Currently he is the head of the department of Quantum and Computer Engineering (QCE) at Delft University of Technology. He is also part-time affiliated with the Cyber Security Technologies group at TNO