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.

  • Eigenvalues of subgraphs of the cube

    BBB. BollobásJLSL European Journal of Combinatorics

    Hypercube eigenvalues

    Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.

  • Spectral partitioning in equitable graphs

    PBP. Barucca Physical Review E

    Spectral partitioning

    The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.

  • Bounds on transient instability for complex ecosystems

    FCF. CaravelliPS PLoS ONE

    Instability in complex ecosystems

    The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.

  • Eigenvalues of neutral networks: Interpolating between hypercubes

    TRT. ReevesRFR. FarrJBJ. BlundellAGA. GallagherTFT. Fink Discrete Mathematics

    Eigenvalues of neutral networks

    The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.

  • EPL

    Robust and assortative

    Spectral analysis shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize.