Algorithm 1 .

WL-align signature

Input: graph G; node u; width k; depth ℓ
Output: signature Hu
1: Hu ← empty list	⊳ append right
2: Q ← empty queue	⊳ FIFO data-structure; pop left (get and remove); append right
3: Q ← append π = (u)	⊳ π is the zero-length, single-node path
4: while Q is not empty do
5: π = (u, …, vh) ← pop path from Q
6: Hu ← append f(π)
7: if h < ℓ then	⊳ h is the length of π
8:  πz ← (u, …, vh, z), ∀z ∈ V	⊳ if (vh, z) ∉ E then w(vh, z) = 0 ⇒ f(πz) = 0
9:  z1, …, zn ← nodes s.t. f(πz1) ≥ … ≥ f(πzn)	⊳ ties broken uniformly at random
10:  Q ← append the k paths πz1,…,πzk.
11: end if
12: end while
13: return Hu