Multiplexity analysis of networks using multigraph representations

Multivariate networks comprising several compositional and structural variables can be represented as multigraphs by various forms of aggregations based on vertex attributes. We propose a framework to perform exploratory and confirmatory multiplexity analysis of aggregated multigraphs in order to find relevant associations between vertex and edge attributes. The exploration is performed by comparing frequencies of the different edges within and between aggregated vertex categories, while the confirmatory analysis is performed using derived complexity or multiplexity statistics under different random multigraph models. These statistics are defined by the distribution of edge multiplicities and provide information on the covariation and dependencies of different edges given vertex attributes. The presented approach highlights the need to further analyse and model structural dependencies with respect to edge entrainment. We illustrate the approach by applying it on a well known multivariate network dataset which has previously been analysed in the context of multiplexity.