In this paper we study an interesting class of graph parameters. These parameters arise both from edge coloring models and from limits of vertex coloring models with a fixed number of vertices. Their vertex connection matrices have exponentially bounded rank growth.
Szegedy, B. (2010). Edge coloring models as singular vertex coloring models. In Bolyai Society Mathematical Studies (Vol. 20, pp. 327–336). https://doi.org/10.1007/978-3-642-13580-4_12