A Generative Model for Spatial Complex Networks: Applications to Power Grids and Brain Networks

In this work, we propose a generative model for spatial networks. The central idea of the model is to use empirical data from real-world spatial networks as a foundation for the network structure that is constructed starting from a set of disconnected nodes and assigning the node positions and the links between them based on key topological and spatial features. In particular, for each node, the number of links to add is determined by sampling values from the degree distribution of real-world networks, while the nodes to connect with are randomly selected based on a probability that depends on the distance between the node positions. For the node positions, we propose either leaving them unconstrained or applying one of four physical constraints with varying levels of strictness. The model can be applied to both two- and three-dimensional spaces. As an example of the former, we consider power grids, while for the latter, we study brain networks. In both cases, we show that the model can be effectively applied to generate surrogate networks, providing a useful tool when spatial network data is limited.