Quantifying metadata relevance to network block structure using description length

Network analysis is often enriched by including an examination of node metadata. In the context of understanding the mesoscale of networks it is often assumed that node groups based on metadata and node groups based on connectivity patterns are intrinsically linked. This assumption is increasingly being challenged, whereby metadata might be entirely unrelated to structure or, similarly, multiple sets of metadata might be relevant to the structure of a network in different ways. We propose the metablox tool to quantify the relationship between a network's node metadata and its mesoscale structure, measuring the strength of the relationship and the type of structural arrangement exhibited by the metadata. We show on a number of synthetic and empirical networks that our tool distinguishes relevant metadata and allows for this in a comparative setting, demonstrating that it can be used as part of systematic meta analyses for the comparison of networks from different domains.