On Modeling Shortest Path Length Distribution in Scale-Free Network Topologies

Complex and interconnected systems belonging to biological, social, economic, and technology application fields are generally described through scale-free topology models. In this context, it is essential to characterize the distribution of shortest paths in order to obtain precious insights on the network behavior. Unfortunately, the few contributions available in the current scientific literature require a case by case tuning of model parameters. To bridge this gap, novel Gaussian-based models are proposed hereby, whose parameters can be immediately tuned based on the number of nodes (N) composing the network, only. In this way, given N, it becomes possible to predict the distribution of shortest paths without re-tuning the model for each scenario of interest. The outcomes of the proposed models have been successfully validated and compared with respect to state of the art approaches in a wide set of network topologies. To provide a further insight, the conceived Gaussian-based models have been also evaluated for real Internet topologies, learned from reference datasets. Obtained results highlight that the proposed models is able to reach a good trade-off between level of accuracy and complexity, even for real network configurations.