The Laplacian matrix of the graph G is defined as L(G) =D(G)-A(G), where D(G) =diag(d(v1),d(v2),… ,d(vn)) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix and of G, respectively.The second smallest eigenvalue of L(G) is called the algebraic connectivity of G.In this topic, we consider the effect on the algebraic connectivity of a graph under perturbation, such as deleting or adding edges, subdivision, grafting an edge, removing edges from one vertex to another etc..As an applications of the above results, we consider the order of graphs by the algebraic connectivity.