3\sqrt{N_{\rm int}}$, as expected. However, 30 [*isolated*]{} RSCG’s with $cz \geq 2300\ {\rm km\ s}^{-1}$ also satisfy $N_{n} > N_{\rm int} + 3\sqrt{N_{\rm int}}$ (for $m_{\rm Zw} \leq$ 15.5) — another indication that “isolation” is not physically meaningful.

Figures \[fig:no1\] – \[fig:ss2\] show examples of the embedding of RSCG’s within the large-scale structure of the nearby universe. They show galaxies with redshifts in the interval (300 km s$^{-1}$, 15,000 km s$^{-1}$) in the redshift surveys ($\cdot$) and RSCG centers ($\times$) (including RSCG’s with $cz < $ 2300 km s$^{-1}$). Compact groups generally follow the large-scale distribution of galaxies, often appearing in the densest regions of the survey. However, Figure \[fig:ss2\] shows the seemingly rare example of a compact group in an apparent void.

Most RSCG’s are embedded in larger systems regardless of how “isolated” they appear. The isolation criterion is unphysical: groups with smaller radii are more likely to appear “isolated” mainly because their isolation annuli are smaller. This variation with radius leads to a dependence of density, $n$, on isolation only because density is computed using the group radius; thus the correlation of $\Upsilon$ with $n$ is unphysical. From here on we include all RSCG’s whether they satisfy the 