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.

- Date
- Subject
- Theme
- Journal
- Citations
- Altmetric
- SNIP
- Author

*x*15

Graph theory

### Transitions in loopy graphs

The generation of large graphs with a controllable number of short loops paves the way for building more realistic random networks.

String theory

### QFT and kids’ drawings

Groethendieck's “children’s drawings”, a type of bipartite graph, link number theory, geometry, and the physics of conformal field theory.

Neurocomputing

### Memristive networks

A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.

Graph theory

### Hypercube eigenvalues

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

Graph theory

### Exactly solvable random graphs

An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.

Neurocomputing

### Dynamics of memristors

Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.

Graph theory

### Spectral partitioning

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

Complex networks

### Democracy in networks

Analysis of the hyperbolicity of real-world networks distinguishes between those which are aristocratic and those which are democratic.

Combinatorics, Graph theory

### Erdős-Ko-Rado theorem analogue

A random analogue of the Erdős-Ko-Rado theorem sheds light on its stability in an area of parameter space which has not yet been explored.

Percolation theory

### Maximum percolation time

A simple formula gives the maximum time for an n x n grid to become entirely infected having undergone a bootstrap percolation process.

Network theory

### Easily repairable networks

When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.

Percolation theory

### Percolation on Galton-Watson trees

The critical probability for bootstrap percolation, a process which mimics the spread of an infection in a graph, is bounded for Galton-Watson trees.

Network theory

### Scales in weighted networks

Information theory fixes weighted networks’ degeneracy issues with a generalisation of binary graphs and an optimal scale of link intensities.

Graph theory

### Unbiased randomization

Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.

Graph theory

### Tailored random graph ensembles

New mathematical tools quantify the topological structure of large directed networks which describe how genes interact within a cell.