Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.
Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.
The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.
The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.
The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.
Spectral analysis shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize.