where ω~ is the normalized matrix of the natural frequency; L = [Lij] is the Laplacian matrix with Lij = δijki − Aij and ki=∑j=1NAij; λj is the jth eigenvalue of L, ordered ascendingly; νj is the normalized eigenvector associated with λj; and 〈·, ·〉 denotes the inner product. When a network is synchronizable, J(ω~,L) is approximately zero, and the analytical approximation of the order parameter can be calculated as:
