Intrinsic dimension as a multi-scale summary statistics in network modeling

Complex networks are powerful mathematical tools for modelling and understanding the behaviour of highly interconnected systems. However, existing methods for analyzing these networks focus on local properties (e.g. degree distribution, clustering coefficient) or global properties (e.g. diameter, modularity) and fail to characterize the network structure across multiple scales. In this paper, we introduce a rigorous method for calculating the intrinsic dimension of unweighted networks. The intrinsic dimension is a feature that describes the network structure at all scales, from local to global. We propose using this measure as a summary statistic within an Approximate Bayesian Computation framework to infer the parameters of flexible and multi-purpose mechanistic models that generate complex networks. Furthermore, we present a new mechanistic model that can reproduce the intrinsic dimension of networks with large diameters, a task that has been challenging for existing models.