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.