Eigentime identities of flower networks with multiple branches

For the fractal networks, the eigentime identity is the expected time for a walker going from one node to another. In this paper, we study a family of flower networks that have k parallel paths with lengths m1,m2,…,mk. Let Ct be the eigentime identity of the flower networks in generation t, then the obtained result shows that the eigentime identity is Ct≈(∑i=1kmi)∕(∑i=1kmi−1)t.