& — & —\
10.5 - 10.9 & -0.048$\pm$0.009 & 0.871$\pm$0.014 & & -0.037$\pm$0.031 & 0.894$\pm$0.003 & & -0.060$\pm$0.007 & 0.760$\pm$0.001 & & -0.114$\pm$0.023 & 0.834$\pm$0.017\
$>$10.9 & -0.049$\pm$0.005 & 0.966$\pm$0.008 & & -0.046$\pm$0.025 & 0.974$\pm$0.023 & & -0.038$\pm$0.007 & 0.911$\pm$0.010 & & -0.041$\pm$0.010 & 0.939$\pm$0.014\

![image](f8.eps)

Density Estimation
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In addition to the “background subtraction" method, we also estimate the galaxy overdensity using the $n^{th}$-nearest-neighbor [e.g. @coo07] approach to probe the color$-$density relation as well as to compare with results from the color as a function of the group-centric radius. The overdensity is computed from the surface density normalized by the median surface density for the redshift range where the surface density of a galaxy is derived from the area enclosed by the $sixth$ nearest neighbor on a projected plane from surrounding galaxies within a redshift slice equal to the photometric redshift uncertainty of the sample, i.e. the $z$ slice = $\pm$ $\sigma_{\Delta z/(1+z_s)}$. The photo-$z$ uncertainty of our galaxy sample is $\sigma_{\Delta z/(1+z_s)}$ $\sim$ 0.05 [@lin14], and that is, the $z$ slice = $\pm$ 0.05. In addition, from simulations, it has been demonstrated that photometric redshift datasets are promising for detecting the color$-$density relation [@lai16], and a similar 