Semi clustering algorithm is mentioned in the Google Pregel paper. The score of a semi cluster is calculated using the below formula$\qquad \displaystyle S_c =\frac{I_c - f_BB_c}{\frac{1}{2}V_c(V_c - 1)}$where$I_c$ is sum of the weights of all the internal edges,$B_c$ is the sum of the weights of all the boundary edges,$V_c$ is the number of edges in the semi cluster and$f_b$ is the boundary edge score factor (user defined between 0 and 1).The algorithm is pretty straight forward, but I could not understand how the above formula was derived. Note that the denominator is the number of edges possible between $V_c$ number of vertices.Could someone please explain it?
What is the significance of the semi clustering formula in the Google Pregel paper?
algorithms;graph theory;terminology