Before revision:  With the base Erdos-Renyi framework as a starting point, the current paper provides a significantly more flexible framework by weighting the edge probabilities via control parameters i,j, with i,j\in \{0,1,2\} enumerating the types of possible vertices (zeroth, first, or second order).
After revision:  With the base Erd\H os-R\'enyi framework as a starting point, the current paper provides a significantly more flexible framework by weighting the edge probabilities via control parameters i,j, with i,j\in \{0,1,2\} enumerating the types of possible vertices (zeroth, first, or second order).