A1144
Title: Graphons and modern networks: A unified approach to relational data modelling
Authors: Charles Dufour - EPFL (Switzerland) [presenting]
Sofia Olhede - EPFL (Switzerland)
Abstract: Graphs in the real world rarely speak in binary; edges carry weights, labels, and stories waiting to be told. To truly understand these complex systems, there is a need for more than traditional binary graphs: It's time for a richer language of connectivity. The first estimation method is introduced for decorated/probability graphons, extending graphon models to handle complex interactions in large networks. A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons in describing large and unlabelled networks are clear, they are traditionally used to describe only binary edge information. Decorated graphons were introduced to extend the graphon framework, allowing more complex relationships such as edge weights and types. Yet, there are no existing inference techniques for decorated graphons. The purpose is to develop such an estimation method, extending existing techniques from traditional graphon estimation to accommodate these more complex interactions. The rate of convergence is derived for the method, and it is shown to be consistent with traditional non-parametric theory for compactly supported decorations/edge weights. This advancement extends the scope of graphon estimation to encompass more complex networks, such as multiplex networks and attributed graphs, thereby increasing the understanding of their underlying structures.
