A Map Equation with Metadata: Varying the Role of Attributes in Community Detection

As the No Free Lunch theorem formally states [1], algorithms for detecting communities in networks must make tradeoffs. In this work, we present a method for using metadata to inform tradeoff decisions. We extend the content map equation, which adds metadata entropy to the traditional map equation, by introducing a tuning parameter allowing for explicit specification of the metadata's relative importance in assigning community labels. On synthetic networks, we show how tuning for node metadata relates to the detectability limit, and on empirical networks, we show how increased tuning for node metadata yields increased mutual information with the metadata at a cost in the traditional map equation. Our tuning parameter, like the focusing knob of a microscope, allows users to "zoom in" and "zoom out" on communities with varying levels of focus on the metadata.