Random graphs were first introduced by Erd"os and Renyi and studied extensively since.
Classical random graph models include a uniform random graph, a binomial random graph, and a random graph process.
Other well-studied random graph models include a uniformly distributed regular random graph and a uniformly distributed random graph with a given degree sequence.
We discuss the evolution of a random graph, such as the connectivity, the structure of its components, the phase transition, and the giant component.
We discuss the evolution of a random graph, such as the connectivity, the structure of its components, the phase transition, and the giant component.
Random graphs and random hypergraphs
- The critical phase for random graphs with a given degree sequence
- The order of the giant component of random hypergraphs
- Local limit theorems and the number of connected hypergraphs
Random graph processes
- The connectivity threshold for the min-degree random graph process
- The phase transition of the minimum degree random multigraph process
- The evolution of the min-min random graph process
