A computer algorithm for determining the symmetry of a kinematic chain is developed. The vertex set of the graph generated from the kinematic chain is partitioned into classes of vertices according to certain structural properties in graph theory. Permutations of vertices in each class are selected if they can map the set of edges into the original set of edges corresponding to the class. They are then concatenated with those from other classes. All the permutations that remain after checking the automorphism become the vertex-induced group of the graph, which represents the symmetry of the corresponding kinematic chain.