Before revision:  By utilizing  matrix block-approximation techniques, we propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) models , while being able to meaningfully model local information ( degrees) as well as global information (  clustering coefficient, assortativity, etc.) if desired.
After revision:  By utilizing matrix block-approximation techniques, we propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) models , while being able to meaningfully model local information ( degrees) as well as global information ( e.g., clustering coefficient, assortativity, etc.) if desired.