Synchronic approach to random networks

Zdzislaw Burda

 Abstract:
    We discuss synchronic approach to random networks. In this approach one uses the concept of statistical ensemble~: for a given set graphs one defines a probability measure. Statistical quantities, as for example Hausdorff dimension, or vertex-vertex correlations, are measured as averages over ensemble. We list some analytic results for tree graphs. In particular we show that the Hausdorff dimension for random trees and for random growing trees is completely different even if the two ensembles have indentical vertex distribution. We also present numerical results on random networks with higher transitivity.