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.
An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.
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.
The analysis of real networks which contain many short loops requires novel methods, because they break the assumptions of tree-like models.
Explicit formulae for the Shannon entropies of random graph ensembles provide measures to compare and reproduce their topological features.
A new concept, graph temperature, enables the prediction of distinct topological properties of real-world networks simultaneously.
Information about 10% of the links in a complex network is sufficient to reconstruct its main features and resilience with the fitness model.
A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.
Methods from tailored random graph theory reveal the relation between true biological networks and the often-biased samples taken from them.