Before revision:  The latter includes many well studied network types, such as the maximal independent set (r=0), the maximal strong matching (r=1), the maximal set of independent cycles (r=2), etc. They are easy to identify or construct, and can be completely disconnected (with r = 0) for the most strict isolation, or allow certain degree of connectivities (with r > 0) for more flexible distancing.
After revision:  The latter includes many well studied network types, which are easy to identify or construct, and can be completely disconnected (with r = 0) for the most strict isolation, or allow certain degree of connectivities (with r > 0) for more flexible distancing.