The article introduces the metablox measure to quantify the relationship between node metadata and the mesoscale structure of networks. The key points are:
Network analysis often assumes an intrinsic connection between node metadata and block structure, but this assumption has been challenged. Metadata may be unrelated to structure or multiple sets of metadata may be relevant in different structural ways.
Metablox uses the minimum description length (MDL) principle to measure the strength of the metadata-block structure relationship and the type of structural arrangement (e.g. assortativity, core-periphery) exhibited by the metadata.
Metablox produces a vector γ with elements corresponding to different structural block models (degree-corrected, non-degree-corrected, assortative). Each element measures how well the metadata partition compresses the network compared to the optimal partition, normalized by the maximum significant compression.
Metablox enables comparisons across multiple networks (with the same metadata) and multiple metadata partitions for a single network. This allows investigating scenarios with (I) a single network and multiple metadata, (II) one metadata and multiple networks, and (III) one metadata and multiple networks in the same context.
The article demonstrates the application of metablox on several real-world networks, including law firm interactions, Twitter debates on political topics, and a longitudinal Twitter network on impact investing. The results provide insights into the varying relevance and structural arrangements of different metadata partitions.
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arxiv.org
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