Recursive tree network
A toy model for a growing network is the recursive tree. The tree starts as a single node and at each step in the growth process, one new node is added which makes a single connection, at random, to an existing node.
Assume that the network has grown large enough so that its statistical properties are effectively constant. The fractions of nodes that have connections to exactly 7 other nodes is given by some fraction \(\dfrac ab\), where \(a\) and \(b\) are positive coprime integers. What is the value of \(a + b\)?