MONTE CARLO METHODS FOR GENERATION OF RANDOM GRAPHS

Random graphs are widely used for modeling complex networks. Instead of considering many different models, to study dynamical phenomena on networks, it is desirable to design a general algorithm which produces random graphs with a variety of properties. Here we present a Monte Carlo method based on a random walk in the space of graphs. By ascribing to each graph a statistical weight we can generate networks of different types by tuning the weight function. The algorithm allows in particular to perform multicanonical simulations known, e.g., from spin models.