methodology as used to create halo catalogs within N–body simulations (see Evrard et al. 2002).

9.  This results in a list of clusters, for which a summed total optical luminosity ($z$ and $r$ bands) and a velocity dispersion are computed (see below).

In summary, the C4 algorithm is a semi-parametric implementation of adaptive kernel density estimation. The key difference with this approach, compared to previous cluster–finding algorithms, is that it does not model either the colors of cluster ellipticals ([*e.g.*]{}, Gladders & Yee 2000, Goto et al. 2003), or the properties of the clusters ([*e.g.*]{}, Postman et al. 1996; Kepner et al. 1999; Kim et al. 2002). Instead, the C4 algorithm only demands that the colors of nearby galaxies are the same as the target galaxy. In this way, the C4 algorithm is sensitive to a diverse range of clusters and groups, [*e.g.*]{}, it would detect a cluster dominated by a extremely “blue” population of galaxies (compared to the colors of field galaxies). Therefore, the C4 catalog can be used for studying galaxy evolution in clusters with little fear that the sample is biased against certain types of systems.

### Simulations of the SDSS Data

![The color–magnitude relation for a 