This paper presents an easy and straightforward routing algorithm for WK-re
cursive topologies. The algorithm, based on adaptive routing, takes advanta
ge of the geometric properties of such topologies. Once a source node S and
destination node D have been determined for a message communication, they
characterize, at some level I, two virtual nodes hl-vn(S-D) and hl-vn(D-S)
that respectively contain S but not D and D but not S. Such virtual nodes c
haracterize other N-d-2 (where N-d is the node degree for a fixed topology)
virtual nodes hl-vn(I-SD) of the same level that contain neither S nor D.
Consequently, it is possible to locate N-d-2 triangles whose vertices are t
hese virtual nodes with property to share the same path, called the self-ro
uting path, directly connecting hl-vn(S-D) to hl-vn(D-S). When the self-rou
ting path is unavailable to transmit a message from S to D because of deadl
ock, fault, and congestion conditions, the routing strategy can follow what
we call the triangle rule to deliver it. The proposed communication scheme
has the advantage that 1) it is the same for all three conditions; 2) each
node of a WK-recursive network, to transmit messages, does not require any
information about their presence or location. Furthermore, this routing al
gorithm is able to tolerate up to [N-d(N-d-3)/2 + 1]N-d(l)-1/N-d-1 faulty l
inks.