The objective in Equation (3) maximizes the number of intra-cluster edges and clusters in the graph, and minimizes the number of inter-cluster edges. Equation (4) ensures that an edge can be exclusively an intra- or inter-cluster edge. Equation (5) ensures that each vertex must belong to a cluster. Equation (6) ensures that an intra-cluster edge must have its both endpoints belonging to the same cluster. Equation (7) defines the variable Cj as a cluster head, if any vertex belongs to its respective cluster.