The Hidden-Degree Geometric Block Model

Defining accurate models for real-world social networks is essential across various research fields including sociology, epidemiology, and marketing. Such models serve as indispensable tools to capture the dynamics of phenomena ranging from disease spread to rumor dissemination, encapsulating intricate patterns of interactions among individuals within a population. To this end, a latent geometry and/or hidden degrees can be used to obtain networks that are small-world, highly clustered, and have a scale-free degree distributions. This study aims to integrate group mixing within the framework of latent geometry models. Our approach is based on conceptualizing a graph with a planted partition as the union of different mono- and bipartite subgraphs, for intra- and inter-block edges, respectively. We highlight that the hidden degree – the analogous of the radial coordinate in purely geometric hyperbolic models – must be replaced by a hidden fitness, and that all latent features must be assigned to the nodes once and for all, rather than once for each subgraph. Through extensive simulations, we show that the proposed model generates networks with a unique combination of features, that cannot be obtained with standard geometric models nor with maximum entropy degree-corrected block models.