Scale-free tree graphs are more symmetrical

In this paper, we consider the symmetry of tree graphs, i.e. the size of the automorphism groups. A polynomial time algorithm named MAST is presented for computing the symmetry of tree graphs, and it is the first polynomial algorithm that has been reported so far for solving this problem. A definition of normalized symmetry is also presented. As a metric of symmetry, normalized symmetry can eliminate the effect degree distribution of graphs to symmetry. A diverse variety of tree graphs were considered in this paper. We found that, in contrast to random tree graph models, scale-free tree graphs are richly symmetric.