  We show that, in contrast to classical random graph models, many real-world
complex systems -- including a variety of biological regulatory networks and
technological networks such as the internet -- spontaneously self-organize to a
richly symmetric state. We consider the organizational origins of symmetry and
find that growth with preferential attachment confers symmetry in highly
branched networks. We deconstruct the automorphism group of some real-world
networks and find that some, but not all, real-world symmetry can be accounted
for by branching. We also uncover an intriguing correspondence between the size
of the automorphism group of growing random trees and the random Fibonacci
sequences.
