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

In the on modelling shortest path length distribution in scale-free network project, 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 behaviour. 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 retuning 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 data sets. Obtained results highlight that the proposed models are able to reach a good trade-off between the level of accuracy and complexity, even for real network configurations.

Keywords: Analytical Model, Internet Topology, Network Theory (Graphs), Shortest Path Problem, Telecommunication Network Topology