Before revision:  However, on the one hand, clustering hasn't been considered as an independent variable and is ignored in some previous analysis, where the patterns of the games might be affected by clustering and thus might not be well compared. On the other hand, many simulations for exploring the clustering effects are analytically intractable due to the great complexity of calculation and the difficulty to find proper categorizations on complex spatial structures. In order to explore the solely and fundamental effect of the clustering  , we employ a minimal model where no game is involved and a simple cycle is adopted.
After revision:  However, the clustering , we employ a minimal model where no game is involved and a simple cycle is adopted.